Imagine a bus that covers 180 km in 6 hours. How fast does it go? Time and Distance problems all rest on one small relation between three things: speed, distance and time .
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Q1. By walking at 3/5 of his usual speed, Sonia reaches office 24 minutes later than usual. What is Sonia’s usual time to reach the office?
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Answer: D
Let usual time = T minutes. New speed = 3/5 of the usual speed. Speed and time are inversely related for a fixed distance. So new time = 5/3 of T. Extra time = new time – T = (5-3)/3 x T. This extra time equals 24 minutes. So T = 24 x 3 / 2 = 36 minutes. Check: new time = 5/3 x 36 = 60 minutes. That is 24 minutes more than 36, as expected.
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Q2. By walking at 3/4 of his usual speed, Pooja reaches office 24 minutes later than usual. What is Pooja’s usual time to reach the office?
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Answer: C
Let usual time = T minutes. New speed = 3/4 of the usual speed. Speed and time are inversely related for a fixed distance. So new time = 4/3 of T. Extra time = new time – T = (4-3)/3 x T. This extra time equals 24 minutes. So T = 24 x 3 / 1 = 72 minutes. Check: new time = 4/3 x 72 = 96 minutes. That is 24 minutes more than 72, as expected.
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Q3. By walking at 1/2 of his usual speed, Anjali reaches office 30 minutes later than usual. What is Anjali’s usual time to reach the office?
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Answer: D
Let usual time = T minutes. New speed = 1/2 of the usual speed. Speed and time are inversely related for a fixed distance. So new time = 2/1 of T. Extra time = new time – T = (2-1)/1 x T. This extra time equals 30 minutes. So T = 30 x 1 / 1 = 30 minutes. Check: new time = 2/1 x 30 = 60 minutes. That is 30 minutes more than 30, as expected.
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Q4. By walking at 2/3 of his usual speed, Vivek reaches office 25 minutes later than usual. What is Vivek’s usual time to reach the office?
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Answer: A
Let usual time = T minutes. New speed = 2/3 of the usual speed. Speed and time are inversely related for a fixed distance. So new time = 3/2 of T. Extra time = new time – T = (3-2)/2 x T. This extra time equals 25 minutes. So T = 25 x 2 / 1 = 50 minutes. Check: new time = 3/2 x 50 = 75 minutes. That is 25 minutes more than 50, as expected.
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Q5. A journey is made in three stages: 225 km at 75 km/hr, 20 km at 20 km/hr, 100 km at 100 km/hr. What is the average speed for the entire journey?
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Answer: B
Leg 1: 225 km at 75 km/hr takes 225/75 = 3 hours. Leg 2: 20 km at 20 km/hr takes 20/20 = 1 hours. Leg 3: 100 km at 100 km/hr takes 100/100 = 1 hours. Total distance = 225 + 20 + 100 = 345 km. Total time = 3 + 1 + 1 = 5 hours. Average speed = total distance / total time = 345/5 = 69 km/hr.
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Q6. A journey is made in three stages: 60 km at 30 km/hr, 225 km at 75 km/hr, 75 km at 25 km/hr. What is the average speed for the entire journey?
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Answer: A
Leg 1: 60 km at 30 km/hr takes 60/30 = 2 hours. Leg 2: 225 km at 75 km/hr takes 225/75 = 3 hours. Leg 3: 75 km at 25 km/hr takes 75/25 = 3 hours. Total distance = 60 + 225 + 75 = 360 km. Total time = 2 + 3 + 3 = 8 hours. Average speed = total distance / total time = 360/8 = 45 km/hr.
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Q7. A journey is made in three stages: 200 km at 50 km/hr, 50 km at 50 km/hr, 200 km at 50 km/hr. What is the average speed for the entire journey?
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Answer: D
Leg 1: 200 km at 50 km/hr takes 200/50 = 4 hours. Leg 2: 50 km at 50 km/hr takes 50/50 = 1 hours. Leg 3: 200 km at 50 km/hr takes 200/50 = 4 hours. Total distance = 200 + 50 + 200 = 450 km. Total time = 4 + 1 + 4 = 9 hours. Average speed = total distance / total time = 450/9 = 50 km/hr.
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Q8. A journey is made in three stages: 150 km at 75 km/hr, 40 km at 40 km/hr, 60 km at 30 km/hr. What is the average speed for the entire journey?
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Answer: B
Leg 1: 150 km at 75 km/hr takes 150/75 = 2 hours. Leg 2: 40 km at 40 km/hr takes 40/40 = 1 hours. Leg 3: 60 km at 30 km/hr takes 60/30 = 2 hours. Total distance = 150 + 40 + 60 = 250 km. Total time = 2 + 1 + 2 = 5 hours. Average speed = total distance / total time = 250/5 = 50 km/hr.
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Q9. A journey is made in three stages: 50 km at 25 km/hr, 100 km at 50 km/hr, 100 km at 100 km/hr. What is the average speed for the entire journey?
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Answer: C
Leg 1: 50 km at 25 km/hr takes 50/25 = 2 hours. Leg 2: 100 km at 50 km/hr takes 100/50 = 2 hours. Leg 3: 100 km at 100 km/hr takes 100/100 = 1 hours. Total distance = 50 + 100 + 100 = 250 km. Total time = 2 + 2 + 1 = 5 hours. Average speed = total distance / total time = 250/5 = 50 km/hr.
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Q10. A journey is made in three stages: 200 km at 50 km/hr, 120 km at 40 km/hr, 90 km at 30 km/hr. What is the average speed for the entire journey?
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Answer: A
Leg 1: 200 km at 50 km/hr takes 200/50 = 4 hours. Leg 2: 120 km at 40 km/hr takes 120/40 = 3 hours. Leg 3: 90 km at 30 km/hr takes 90/30 = 3 hours. Total distance = 200 + 120 + 90 = 410 km. Total time = 4 + 3 + 3 = 10 hours. Average speed = total distance / total time = 410/10 = 41 km/hr.
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Q11. A journey is made in three stages: 20 km at 20 km/hr, 240 km at 60 km/hr, 100 km at 25 km/hr. What is the average speed for the entire journey?
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Answer: D
Leg 1: 20 km at 20 km/hr takes 20/20 = 1 hours. Leg 2: 240 km at 60 km/hr takes 240/60 = 4 hours. Leg 3: 100 km at 25 km/hr takes 100/25 = 4 hours. Total distance = 20 + 240 + 100 = 360 km. Total time = 1 + 4 + 4 = 9 hours. Average speed = total distance / total time = 360/9 = 40 km/hr.
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Q12. A journey is made in three stages: 80 km at 20 km/hr, 160 km at 40 km/hr, 240 km at 60 km/hr. What is the average speed for the entire journey?
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Answer: C
Leg 1: 80 km at 20 km/hr takes 80/20 = 4 hours. Leg 2: 160 km at 40 km/hr takes 160/40 = 4 hours. Leg 3: 240 km at 60 km/hr takes 240/60 = 4 hours. Total distance = 80 + 160 + 240 = 480 km. Total time = 4 + 4 + 4 = 12 hours. Average speed = total distance / total time = 480/12 = 40 km/hr.
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Q13. A journey is made in three stages: 30 km at 30 km/hr, 90 km at 30 km/hr, 60 km at 30 km/hr. What is the average speed for the entire journey?
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Answer: B
Leg 1: 30 km at 30 km/hr takes 30/30 = 1 hours. Leg 2: 90 km at 30 km/hr takes 90/30 = 3 hours. Leg 3: 60 km at 30 km/hr takes 60/30 = 2 hours. Total distance = 30 + 90 + 60 = 180 km. Total time = 1 + 3 + 2 = 6 hours. Average speed = total distance / total time = 180/6 = 30 km/hr.
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Q14. A journey is made in three stages: 160 km at 40 km/hr, 200 km at 100 km/hr, 120 km at 60 km/hr. What is the average speed for the entire journey?
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Answer: D
Leg 1: 160 km at 40 km/hr takes 160/40 = 4 hours. Leg 2: 200 km at 100 km/hr takes 200/100 = 2 hours. Leg 3: 120 km at 60 km/hr takes 120/60 = 2 hours. Total distance = 160 + 200 + 120 = 480 km. Total time = 4 + 2 + 2 = 8 hours. Average speed = total distance / total time = 480/8 = 60 km/hr.
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Q15. A journey is made in three stages: 90 km at 30 km/hr, 90 km at 30 km/hr, 60 km at 30 km/hr. What is the average speed for the entire journey?
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Answer: C
Leg 1: 90 km at 30 km/hr takes 90/30 = 3 hours. Leg 2: 90 km at 30 km/hr takes 90/30 = 3 hours. Leg 3: 60 km at 30 km/hr takes 60/30 = 2 hours. Total distance = 90 + 90 + 60 = 240 km. Total time = 3 + 3 + 2 = 8 hours. Average speed = total distance / total time = 240/8 = 30 km/hr.
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Q16. A journey is made in three stages: 80 km at 40 km/hr, 100 km at 50 km/hr, 40 km at 40 km/hr. What is the average speed for the entire journey?
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Answer: A
Leg 1: 80 km at 40 km/hr takes 80/40 = 2 hours. Leg 2: 100 km at 50 km/hr takes 100/50 = 2 hours. Leg 3: 40 km at 40 km/hr takes 40/40 = 1 hours. Total distance = 80 + 100 + 40 = 220 km. Total time = 2 + 2 + 1 = 5 hours. Average speed = total distance / total time = 220/5 = 44 km/hr.
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Q17. On a certain journey, a traveller covers 1/4 of the total distance at 40 km/hr, 1/4 of the total distance at 24 km/hr, and the rest at 15 km/hr. What is the average speed for the whole journey?
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Answer: B
Let the total distance be D = 4 km. Distance at 40 km/hr = 1/4 x 4 = 1 km. Distance at 24 km/hr = 1/4 x 4 = 1 km. Distance at 15 km/hr = the rest = 2 km. Time for each leg = distance / speed. Time 1 = 1/40 = 0.03 hours. Time 2 = 1/24 = 0.04 hours. Time 3 = 2/15 = 0.13 hours. Total time = 0.03 + 0.04 + 0.13 = 0.2 hours. Average speed = total distance / total time = 4/0.2 = 20 km/hr.
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Q18. On a certain journey, a traveller covers 1/5 of the total distance at 10 km/hr, 2/5 of the total distance at 20 km/hr, and the rest at 15 km/hr. What is the average speed for the whole journey?
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Answer: D
Let the total distance be D = 5 km. Distance at 10 km/hr = 1/5 x 5 = 1 km. Distance at 20 km/hr = 2/5 x 5 = 2 km. Distance at 15 km/hr = the rest = 2 km. Time for each leg = distance / speed. Time 1 = 1/10 = 0.1 hours. Time 2 = 2/20 = 0.1 hours. Time 3 = 2/15 = 0.13 hours. Total time = 0.1 + 0.1 + 0.13 = 0.33 hours. Average speed = total distance / total time = 5/0.33 = 15 km/hr.
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Q19. On a certain journey, a traveller covers 1/5 of the total distance at 15 km/hr, 1/5 of the total distance at 20 km/hr, and the rest at 60 km/hr. What is the average speed for the whole journey?
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Answer: C
Let the total distance be D = 5 km. Distance at 15 km/hr = 1/5 x 5 = 1 km. Distance at 20 km/hr = 1/5 x 5 = 1 km. Distance at 60 km/hr = the rest = 3 km. Time for each leg = distance / speed. Time 1 = 1/15 = 0.07 hours. Time 2 = 1/20 = 0.05 hours. Time 3 = 3/60 = 0.05 hours. Total time = 0.07 + 0.05 + 0.05 = 0.17 hours. Average speed = total distance / total time = 5/0.17 = 30 km/hr.
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Q20. On a certain journey, a traveller covers 1/5 of the total distance at 15 km/hr, 2/5 of the total distance at 30 km/hr, and the rest at 10 km/hr. What is the average speed for the whole journey?
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Answer: A
Let the total distance be D = 5 km. Distance at 15 km/hr = 1/5 x 5 = 1 km. Distance at 30 km/hr = 2/5 x 5 = 2 km. Distance at 10 km/hr = the rest = 2 km. Time for each leg = distance / speed. Time 1 = 1/15 = 0.07 hours. Time 2 = 2/30 = 0.07 hours. Time 3 = 2/10 = 0.2 hours. Total time = 0.07 + 0.07 + 0.2 = 0.33 hours. Average speed = total distance / total time = 5/0.33 = 15 km/hr.
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Q21. On a certain journey, a traveller covers 1/5 of the total distance at 15 km/hr, 1/5 of the total distance at 20 km/hr, and the rest at 10 km/hr. What is the average speed for the whole journey?
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Answer: B
Let the total distance be D = 5 km. Distance at 15 km/hr = 1/5 x 5 = 1 km. Distance at 20 km/hr = 1/5 x 5 = 1 km. Distance at 10 km/hr = the rest = 3 km. Time for each leg = distance / speed. Time 1 = 1/15 = 0.07 hours. Time 2 = 1/20 = 0.05 hours. Time 3 = 3/10 = 0.3 hours. Total time = 0.07 + 0.05 + 0.3 = 0.42 hours. Average speed = total distance / total time = 5/0.42 = 12 km/hr.
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Q22. On a certain journey, a traveller covers 1/3 of the total distance at 15 km/hr, 1/5 of the total distance at 20 km/hr, and the rest at 60 km/hr. What is the average speed for the whole journey?
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Answer: B
Let the total distance be D = 15 km. Distance at 15 km/hr = 1/3 x 15 = 5 km. Distance at 20 km/hr = 1/5 x 15 = 3 km. Distance at 60 km/hr = the rest = 7 km. Time for each leg = distance / speed. Time 1 = 5/15 = 0.33 hours. Time 2 = 3/20 = 0.15 hours. Time 3 = 7/60 = 0.12 hours. Total time = 0.33 + 0.15 + 0.12 = 0.6 hours. Average speed = total distance / total time = 15/0.6 = 25 km/hr.
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Q23. On a certain journey, a traveller covers 2/5 of the total distance at 30 km/hr, 1/5 of the total distance at 20 km/hr, and the rest at 40 km/hr. What is the average speed for the whole journey?
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Answer: D
Let the total distance be D = 5 km. Distance at 30 km/hr = 2/5 x 5 = 2 km. Distance at 20 km/hr = 1/5 x 5 = 1 km. Distance at 40 km/hr = the rest = 2 km. Time for each leg = distance / speed. Time 1 = 2/30 = 0.07 hours. Time 2 = 1/20 = 0.05 hours. Time 3 = 2/40 = 0.05 hours. Total time = 0.07 + 0.05 + 0.05 = 0.17 hours. Average speed = total distance / total time = 5/0.17 = 30 km/hr.
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Q24. On a certain journey, a traveller covers 1/5 of the total distance at 30 km/hr, 2/5 of the total distance at 24 km/hr, and the rest at 40 km/hr. What is the average speed for the whole journey?
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Answer: C
Let the total distance be D = 5 km. Distance at 30 km/hr = 1/5 x 5 = 1 km. Distance at 24 km/hr = 2/5 x 5 = 2 km. Distance at 40 km/hr = the rest = 2 km. Time for each leg = distance / speed. Time 1 = 1/30 = 0.03 hours. Time 2 = 2/24 = 0.08 hours. Time 3 = 2/40 = 0.05 hours. Total time = 0.03 + 0.08 + 0.05 = 0.17 hours. Average speed = total distance / total time = 5/0.17 = 30 km/hr.
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Q25. On a certain journey, a traveller covers 1/4 of the total distance at 30 km/hr, 1/3 of the total distance at 24 km/hr, and the rest at 15 km/hr. What is the average speed for the whole journey?
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Answer: A
Let the total distance be D = 12 km. Distance at 30 km/hr = 1/4 x 12 = 3 km. Distance at 24 km/hr = 1/3 x 12 = 4 km. Distance at 15 km/hr = the rest = 5 km. Time for each leg = distance / speed. Time 1 = 3/30 = 0.1 hours. Time 2 = 4/24 = 0.17 hours. Time 3 = 5/15 = 0.33 hours. Total time = 0.1 + 0.17 + 0.33 = 0.6 hours. Average speed = total distance / total time = 12/0.6 = 20 km/hr.
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