A boat can travel downstream at 20 km/h and upstream at 16 km/h. What is the speed of the stream?
- 18 km/h
- 2 km/h
- 5 km/h
- 4 km/h
Explanation: Speed of stream = (Downstream speed - Upstream speed) / 2 = (20 - 16) / 2 = 2 km/h.
A boat covers a certain distance downstream at 20 km/h and returns upstream at 14 km/h. What is the speed of the boat in still water?
- 18 km/h
- 3 km/h
- 17 km/h
- 34 km/h
Explanation: Speed in still water = (Downstream speed + Upstream speed) / 2 = (20 + 14) / 2 = 17 km/h.
A boat takes 4 hours to travel 80 km downstream and 8 hours to return upstream. What is the ratio of the speed of the boat in still water to the speed of the stream?
Explanation: Downstream speed = 80/4 = 20 km/h. Upstream speed = 80/8 = 10 km/h. Boat speed = (20+10)/2 = 15 km/h. Stream speed = (20-10)/2 = 5 km/h. Ratio = 15:5.
A boat's speed in still water is 12 km/h and the stream flows at 3 km/h. The boat takes 8/3 hours more to travel a certain distance upstream than downstream. What is the distance?
Explanation: Downstream speed = 15 km/h, upstream speed = 9 km/h. Time difference = D/(b-s) - D/(b+s) = 8/3. Solving: D × (2s)/(b²-s²) = 8/3, so D = 60 km.
A boat travels 72 km downstream and returns the same distance upstream. If the boat's speed in still water is 13 km/h and the stream speed is 3 km/h, what is the average speed for the entire journey?
- 10 km/h
- 160/13 km/h
- 13 km/h
- 16 km/h
Explanation: Average speed for equal distances = 2×Down×Up/(Down+Up) = 2×16×10/(16+10) = 160/13 km/h.
Two boats start simultaneously from opposite ends of a 150 km river. Boat A moves downstream at 15 km/h and Boat B moves upstream at 7 km/h. After how many hours will they meet?
- 75/11 hours
- 60/7 hours
- 18 hours
- 20/9 hours
Explanation: Relative speed = sum of speeds = 15 + 7 = 22 km/h. Time = Distance/Relative speed = 150/22 = 75/11 hours.
A man can row 16 km downstream at 8 km/h. On a particular day, he covers the same distance in 4 hours. How long did he rest?
- 2 hours
- 3 hours
- 4 hours
- 1 hour
Explanation: Normal time = Distance/Speed = 16/8 = 2 hours. Rest time = Actual time - Normal time = 4 - 2 = 2 hours.
The ratio of time taken by a boat to travel a certain distance downstream to that upstream is 2:1. If the stream speed is 5 km/h, what is the boat's speed in still water?
- 10 km/h
- 18 km/h
- 20 km/h
- 15 km/h
Explanation: Time ratio is inverse of speed ratio. So (b+s)/(b-s) = 2/1. Solving: 1(b+s) = 2(b-s) gives b = 15 km/h.
A boat travels 45 km downstream and 30 km upstream. The boat's speed in still water is 14 km/h and the stream flows at 4 km/h. What is the total time taken?
- 91/15 hours
- 12/5 hours
- 76/15 hours
- 5 hours
Explanation: Downstream time = 45/18 = 5/2 hours. Upstream time = 30/10 = 3 hours. Total = 76/15 hours.
A boat with speed 12 km/h in still water moves in a stream of 4 km/h. It takes 9 hours to go downstream to a point and return. What is the distance to that point?
Explanation: Let distance be D. Then D/(b+s) + D/(b-s) = Total time. D × [1/16 + 1/8] = 9. Solving gives D = 48 km.
A boat (speed 15 km/h in still water) travels 60 km downstream and returns. If the stream speed increases from 3 km/h to 5 km/h, by what percentage does the total time increase?
Explanation: Original time = 60/18 + 60/12 = 25/3 hours. New time = 60/20 + 60/10 = 9 hours. Percentage increase = (9-25/3)/(25/3) × 100 = 8%.
A boat (speed 10 km/h in still water) starts from A, goes 60 km downstream to B, and returns to A. A raft starts from A at the same time and drifts to B at stream speed 5 km/h. How much later does the boat return to A compared to the raft reaching B?
- 16 hours
- 4 hours
- 12 hours
- 6 hours
Explanation: Raft time = 60/5 = 12 hours. Boat time = 60/15 + 60/5 = 4 + 12 = 16 hours. Difference = 4 hours.
Two boats start from the same point going downstream. Boat A has speed 14 km/h in still water and Boat B has 10 km/h. The stream is 3 km/h. If Boat A is 60 km behind Boat B, after how many hours will it catch up?
- 60/7 hours
- 15 hours
- 20/9 hours
- 18 hours
Explanation: Both move downstream, so stream speed cancels out. Relative speed = 14-10 = 4 km/h. Time = 60/4 = 15 hours.
A boat travels 36 km downstream in a stream of 3 km/h, then 24 km upstream. The boat's speed in still water is 12 km/h. What is the total time?
- 91/15 hours
- 76/15 hours
- 12/5 hours
- 5 hours
Explanation: Downstream time = 36/15 = 12/5 hours. Upstream time = 24/9 = 8/3 hours. Total = 76/15 hours.
A boat with speed 11 km/h in still water travels 72 km downstream and returns, taking 99/7 hours total. What is the stream speed?
- 5 km/h
- 8 km/h
- 3 km/h
- 6 km/h
Explanation: Let stream speed be s. Then 72/(11+s) + 72/(11-s) = 99/7. Solving the equation yields s = 3 km/h.
A boat moves at 20 km/h downstream and 14 km/h upstream. A student calculates the average of these two speeds as the boat's speed in still water. What is the actual speed in still water?
- 16 km/h
- 20 km/h
- 14 km/h
- 17 km/h
Explanation: Speed in still water = (Downstream speed + Upstream speed) / 2 = (20 + 14) / 2 = 17 km/h.
A boat with speed 18 km/h in still water moves in a stream of 6 km/h. What is the ratio of time taken to cover 120 km upstream to that downstream?
Explanation: Time upstream = 120/12 = 10 hours. Time downstream = 120/24 = 5 hours. Ratio = 10:5 = 2:1.
A man rows 36 km downstream at boat speed 10 km/h in still water (stream 3 km/h), then walks 15 km at 5 km/h. What is the total time?
- 76/15 hours
- 75/13 hours
- 36/13 hours
- 3 hours
Explanation: Rowing time = 36/13 hours. Walking time = 15/5 = 3 hours. Total = 36/13 + 3 = 75/13 hours.
A boat travels 35 km downstream with stream speed 3 km/h, then 45 km downstream with stream speed 5 km/h. The boat's speed in still water is 12 km/h. What is the total time?
- 254/51 hours
- 98/15 hours
- 35/15 hours
- 80/17 hours
Explanation: First segment time = 35/15 = 7/3 hours. Second segment time = 45/17 hours. Total = 7/3 + 45/17 = 254/51 hours.
A boat goes 40 km downstream and 30 km upstream. Speed in still water is 14 km/h, stream is 4 km/h. What is the average speed for the entire journey?
- 14 km/h
- 35 km/h
- 630/47 km/h
- 47/9 hours
Explanation: Total distance = 70 km. Total time = 40/18 + 30/10 = 47/9 hours. Average speed = Total distance/Total time = 630/47 km/h.
Two boats start from the same point on a river. Boat A goes upstream at 9 km/h and Boat B goes downstream at 13 km/h. After how many hours will they be 100 km apart?
- 102/22 hours
- 100/2 hours
- 100/25 hours
- 50/11 hours
Explanation: Relative speed = 9 + 13 = 22 km/h (moving in opposite directions). Time = 100/22 = 50/11 hours.
A boat with speed 14 km/h in still water takes 15/2 hours to go downstream to a point and return upstream. The stream speed is 4 km/h. What is the distance to that point?
Explanation: Let distance be D. D/(b+s) + D/(b-s) = Total time. D × [1/18 + 1/10] = 15/2. Solving gives D = 72 km.
A boat takes 3 hours to travel 48 km downstream and 6 hours to return. What is the speed of the boat in still water?
- 16 km/h
- 8 km/h
- 12 km/h
- 15 km/h
Explanation: Downstream speed = 48/3 = 16 km/h. Upstream speed = 48/6 = 8 km/h. Still water speed = (16+8)/2 = 12 km/h.
A boat with speed 4 km/h in still water (stream 2 km/h) travels 12 km downstream and back. If the boat's speed doubles, how many hours are saved?
- 12/5 hours
- 16/5 hours
- 24/5 hours
- 8 hours
Explanation: Original time = 12/6 + 12/2 = 2 + 6 = 8 hours. New time = 12/10 + 12/6 = 6/5 + 2 = 16/5 hours. Time saved = 8 - 16/5 = 24/5 hours.
A boat travels downstream at speed 18 km/h. The ratio of downstream to upstream speed is 3:2. If downstream journey takes 4 hours, what is the distance?
Explanation: Distance = Speed × Time = 18 × 4 = 72 km.
A man can swim at 8 km/h in still water. He swims 20 km downstream and returns. The stream flows at 3 km/h. What is the total time?
- 5 hours
- 20/11 hours
- 80/11 hours
- 64/11 hours
Explanation: Downstream time = 20/11 hours. Upstream time = 20/5 = 4 hours. Total = 20/11 + 44/11 = 64/11 hours.
A boat with speed 12 km/h in still water takes 80/7 hours for a round trip of 80 km and 120/7 hours for a round trip of 100 km. What is the stream speed?
- 3 km/h
- 5 km/h
- 12 km/h
- 9 km/h
Explanation: Round trip time for distance D is D/(b+s) + D/(b-s) = 2Db/(b²-s²). Using the two given distances and times, solving simultaneously yields stream speed s = 3 km/h.
Two boats are at opposite ends of an 80 km river. Boat A (10 km/h downstream) starts immediately. Boat B (4 km/h upstream) starts 1 hour later. How far from A's starting point do they meet?
Explanation: In 1 hour, A covers 10 km. Remaining distance = 70 km. Relative speed = 10 + 4 = 14 km/h. Time to meet after B starts = 70/14 = 5 hours. Distance from A = 10 + 10×5 = 60 km.
A boat travels 30 km across a lake at 12 km/h, then 60 km downstream in a stream of 4 km/h. What is the total time?
- 10/2 hours
- 15/4 hours
- 5/2 hours
- 25/4 hours
Explanation: Lake time = 30/12 = 5/2 hours. Downstream time = 60/16 = 15/4 hours. Total = 5/2 + 15/4 = 10/4 + 15/4 = 25/4 hours.
A boat travels for 4 hours downstream and then 4 hours upstream. What is the ratio of distance covered downstream to that upstream?
Explanation: Distance downstream = 16 × 4 = 64 km. Distance upstream = 8 × 4 = 32 km. Ratio = 64:32 = 2:1.
Two runners A and B start from the same point on a circular track of length 400 m. A runs at 20 m/s and B at 12 m/s in the same direction. After how many seconds will A overtake B for the first time?
- 400/32 seconds
- 55 seconds
- 400/20 seconds
- 50 seconds
Explanation: For same direction, relative speed = 20-12 = 8 m/s. Time to first meeting = Track length / Relative speed = 400/8 = 50 seconds.
Two runners start from the same point on a circular track of 500 m and run in opposite directions at 15 m/s and 10 m/s. When will they first meet?
- 500/15 seconds
- 20 seconds
- 500/25 seconds
- 500/5 seconds
Explanation: For opposite directions, relative speed = 15+10 = 25 m/s. Time to first meeting = 500/25 = 20 seconds.
Two runners start together on a 500 m circular track and run in the same direction at 20 m/s and 15 m/s. After how many seconds will they meet for the 3rd time?
- 1500/35 seconds
- 100 seconds
- 150 seconds
- 300 seconds
Explanation: For same direction, each meeting requires the faster to gain one full lap. Time for nth meeting = n × L / Relative speed = 3×500/(20-15) = 300 seconds.
Two runners start from the same point on a 400 m track and run in opposite directions at 14 m/s and 10 m/s. When is their 3rd meeting?
- 50 seconds
- 400/24 seconds
- 125 seconds
- 1200/4 seconds
Explanation: For opposite directions, each meeting requires combined distance of one lap. Time for nth meeting = n × L / (a+b) = 3×400/(14+10) = 1200/24 = 50 seconds.
Two runners start together on a 400 m circular track running in the same direction at 20 m/s and 12 m/s. How many times do they meet in 120 seconds?
- 3 times
- 4 times
- 2 times
- 9 times
Explanation: Relative speed = 20 - 12 = 8 m/s. Total relative distance = 8 × 120 = 960 m. Number of meetings = 960 / 400 = 2.4, which means 2 complete meetings.
Two runners start from the same point on a 500 m track and run in opposite directions at 15 m/s and 10 m/s. How many times do they meet in 100 seconds?
- 5 times
- 4 times
- 6 times
- 1 time
Explanation: Relative speed = 25 = 25 m/s. Total relative distance = 25×100 = 2500 m. Number of meetings = 2500/500 = 5.
On a 400 m circular track, runner A starts at speed 16 m/s and runner B at 10 m/s in the same direction, with B 100 m ahead of A. When does A first catch B?
- 400/6 seconds
- 70 seconds
- 100/6 seconds
- 50 seconds
Explanation: A must gain 400 - 100 = 300 m on B to catch up from behind. Relative speed = 16 - 10 = 6 m/s. Time = 300 / 6 = 50 seconds.
Two runners start at points 90 m apart on a 300 m circular track and run in opposite directions at 12 m/s and 8 m/s. When do they first meet?
- 92 seconds
- 210/20 seconds
- 9/2 seconds
- 300/20 seconds
Explanation: Since they run opposite directions and start 90 m apart along the shorter arc, they meet when combined distance equals 90 m. Relative speed = 20 m/s. Time = 90/20 = 9/2 seconds.
Two runners start together and run in the same direction. Their speeds are 20 m/s and 15 m/s. They meet every 100 seconds. What is the track length?
- 2000 m
- 500 m
- 450 m
- 3500 m
Explanation: For same direction, track length = Relative speed × Time between meetings = (20-15) × 100 = 500 m.
On a 600 m circular track, two runners start together running in the same direction. One runs at 18 m/s and they meet every 100 seconds. What is the slower runner's speed?
- 12 m/s
- 13 m/s
- 6 m/s
- 16 m/s
Explanation: For same direction, relative speed = Track length / Time = 600/100 = 6 m/s. Slower speed = 18 - 6 = 12 m/s.
Two runners starting together on a 400 m track meet every 50 seconds when running in the same direction and every 10 seconds when running in opposite directions. What is the ratio of their speeds?
Explanation: Let speeds be a and b. Same direction: L/(a-b) = 50. Opposite: L/(a+b) = 10. Solving gives a = 24 m/s and b = 16 m/s. Ratio = 24:16.
Two runners start together and run in the same direction on a circular track at 20 m/s and 12 m/s. How many distinct points on the track do they meet?
- 2 points
- 150 points
- 4 points
- 8 points
Explanation: Number of distinct meeting points = |a-b| / gcd(a,b) = |20-12| / 4 = 2.
Two runners start together on a 500 m track running in the same direction at 15 m/s and 10 m/s. How many laps has the faster runner completed when they meet for the 3rd time?
- 2 laps
- 3 laps
- 4 laps
- 9 laps
Explanation: Time for 3rd meeting = 3×500/(15-10) = 300 seconds. Distance by faster runner = 15×300 = 4500 m. Laps = 4500/500 = 9.
On a 400 m track, runner A (20 m/s) and B (12 m/s) start together running in the same direction. After 20 seconds, A stops. How many total seconds after the start does B catch A?
- 100/3 seconds
- 33 seconds
- 40/3 seconds
- 20 seconds
Explanation: In 20 seconds, A reaches 400 m mark (0 m from start) and B reaches 240 m mark. B must cover 160 m more to reach A at 0 m. Time for B = 160/12 = 40/3 seconds. Total = 20 + 40/3 = 100/3 seconds.
Three runners start together on a 600 m track running in the same direction at 20 m/s, 15 m/s, and 12 m/s. After how many seconds will all three be together again at the starting point?
- 700 seconds
- 600 seconds
- 120 seconds
- 75 seconds
Explanation: A and B meet every 600/5 = 120 seconds. B and C every 600/3 = 200 seconds. A and C every 600/8 = 75 seconds. All three meet at LCM(120, 200, 75) = 600 seconds.
On a 400 m track, runner A completes a lap in 16 seconds. Running in the same direction with B, they meet every 40 seconds. What is B's speed?
- 25 m/s
- 20 m/s
- 10 m/s
- 15 m/s
Explanation: A's speed = 400/16 = 25 m/s. Relative speed = 400/40 = 10 m/s. B's speed = 25 - 10 = 15 m/s.
Two runners start 100 m apart on a 500 m circular track and run in opposite directions at 18 m/s and 12 m/s. When is their second meeting?
- 100/30 seconds
- 20 seconds
- 500/30 seconds
- 35 seconds
Explanation: First meeting when combined distance = 100 m. Second meeting requires combined distance = 600 m. Relative speed = 30 m/s. Time = 600/30 = 20 seconds.
Two runners start together on a 400 m track running in the same direction at 20 m/s and 12 m/s. After how many seconds do they meet at the point diametrically opposite to the start?
- 25 seconds
- 50 seconds
- 100/8 seconds
- 40 seconds
Explanation: They meet when relative distance is a multiple of 400 m. Relative speed = 8 m/s. First meeting at 50 seconds. At t = 50 seconds, faster has covered 1000 m (200 m from start) and slower 600 m (200 m from start). Both are at 200 m mark.
A runner completes the first lap of a 300 m track at 15 m/s and the second lap at 10 m/s. What is the average speed for the two laps?
- 10 m/s
- 15 m/s
- 12 m/s
- 12.5 m/s
Explanation: Total distance = 600 m. Total time = 300/15 + 300/10 = 50 seconds. Average speed = 600/50 = 12 m/s.
Two runners start together on a 400 m track and run in opposite directions at 16 m/s and 12 m/s. After how many seconds will they both be at the starting point simultaneously?
- 100 seconds
- 100/4 seconds
- 200/3 seconds
- 25 seconds
Explanation: Runner A returns to start every 400/16 = 25 seconds. Runner B every 400/12 = 100/3 seconds. They are at start together at LCM(25, 100/3) = 100 seconds.
On a 400 m track, runner A (20 m/s) and runner B (10 m/s) start together running in the same direction. How many times does A overtake B before B completes his first lap?
- 3 times
- 2 times
- 0 times
- 1 time
Explanation: B completes one lap in 400/10 = 40 seconds. In 40 seconds, A covers 20×40 = 800 m = 2 laps. A overtakes B 2-1 = 1 time before B finishes.
Two runners start from the same point on a 500 m track and run in opposite directions at 15 m/s and 10 m/s. How far from the start is their first meeting point?
Explanation: Time to first meeting = 500/25 = 20 seconds. Distance from start by runner A = 15×20 = 300 m.
Two runners start together on a 400 m track running in the same direction at 20 m/s and 12 m/s. How far from the start is their 2nd meeting point?
Explanation: Time for 2nd meeting = 2×400/8 = 100 seconds. Distance covered by A = 20×100 = 2000 m. Position = 2000 mod 400 = 0 m.
Two runners start together on a circular track running in the same direction at 18 m/s and 12 m/s. They first meet at the point diametrically opposite to the start after 50 seconds. What is the track length?
Explanation: To meet at the diametrically opposite point, the faster must gain half a lap on the slower. Relative speed = 6 m/s. Half lap = 6×50 = 300 m. Full lap = 600 m.
Three runners start together on a 300 m track running in the same direction at 15 m/s, 10 m/s, and 6 m/s. After how many seconds will A and B meet while C is exactly at the starting point?
- 350 seconds
- 60 seconds
- 300 seconds
- 50 seconds
Explanation: A and B meet every 300/5 = 60 seconds. C is at start every 300/6 = 50 seconds. Both conditions occur at LCM(60, 50) = 300 seconds.
Two runners start from the same point on a 400 m track and run in opposite directions at 16 m/s and 12 m/s. What is the ratio of distances covered by them till their first meeting?
Explanation: They run for the same time until meeting. Distance ratio = speed ratio = 16:12 = 4:3.
Two runners start together on a 500 m track running in the same direction at 18 m/s and 12 m/s. What is the distance between them along the track after 80 seconds?
Explanation: Relative distance gained = 6×80 = 480 m. On a circular track, distance between them = 480 mod 500 = 480 m.
On a 600 m track, two runners start together running in the same direction. The faster runs at 20 m/s and they meet 3 times in 300 seconds. What is the slower runner's speed?
- 15 m/s
- 10 m/s
- 14 m/s
- 6 m/s
Explanation: Number of meetings = Relative speed × Time / Track length. So 3 = (a-b)×300/600. Solving: a-b = 6 m/s. b = 20 - 6 = 14 m/s.
Two runners start from the same point on a 400 m track and run in opposite directions at 20 m/s and 15 m/s. How far from the start is their second meeting point?
Explanation: Second meeting occurs when combined distance = 800 m. Time = 800/35 = 160/7 seconds. Distance by A = 20×160/7 = 3200/7 ≈ 457.14 m. Position = 457.14 mod 400 = 57.14 m ≈ 57 m.
Two runners start together on a 500 m track running in the same direction at 25 m/s and 15 m/s. After how many seconds is the faster runner exactly one full lap ahead of the slower?
- 50 seconds
- 25/2 seconds
- 60 seconds
- 100 seconds
Explanation: To be one full lap ahead, the faster must gain 500 m on the slower. Relative speed = 10 m/s. Time = 500/10 = 50 seconds.