Time and Distance— Concepts, Formulas & Shortcuts
- Distance = Speed × Time; Speed = Distance/Time; Time = Distance/Speed.
- x km/h = x × 5/18 m/s.
- Constant distance → speed and time are inversely proportional. Speed ratio a : b ⇒ time ratio b : a.
- Average speed for equal distances at speeds u and v = 2uv/(u + v) — the harmonic mean, never (u + v)/2.
- Average speed for equal times = (u + v)/2.
- Early/late problems: the difference between the two travel times equals the total time gap.
Time and Distance Practice Questions with Answers
Attempt each question first, then open the explanation. All 28 questions below are free to read and require no signup.
Q1.A man walks 6 km in 1 hour 15 minutes. His speed is:
Easy- A4.5 km/h
- B4.8 km/h
- C5 km/h
- D5.2 km/h
Time and Distance question 1 of 28+Show Answer & Explanation
Answer: B. 4.8 km/h
Explanation: 1 h 15 min = 1.25 h. Speed = 6/1.25 = 4.8 km/h.
Q2.A car covers a distance at 40 km/h and returns along the same route at 60 km/h. Its average speed for the whole journey is:
Moderate- A48 km/h
- B50 km/h
- C52 km/h
- D54 km/h
Time and Distance question 2 of 28+Show Answer & Explanation
Answer: A. 48 km/h
Explanation: Equal distances → average = 2uv/(u+v) = 2 × 40 × 60/100 = 48 km/h. It is NOT 50.
Q3.Walking at 3/4 of his usual speed, a man reaches office 20 minutes late. His usual time is:
Moderate- A45 min
- B50 min
- C60 min
- D75 min
Time and Distance question 3 of 28+Show Answer & Explanation
Answer: C. 60 min
Explanation: Speed becomes 3/4 → time becomes 4/3 of usual. Extra time = 1/3 × T = 20 min → T = 60 minutes.
Q4.A person crosses a 600 m long street in 5 minutes. His speed in km/h is:
Easy- A3.6
- B7.2
- C8.4
- D10
Time and Distance question 4 of 28+Show Answer & Explanation
Answer: B. 7.2
Explanation: 600 m in 300 s = 2 m/s = 2 × 18/5 = 7.2 km/h.
Q5.A train covers 200 km in 4 hours. To cover the same distance in 2 hours 30 minutes, its speed must be:
Easy- A70 km/h
- B75 km/h
- C80 km/h
- D85 km/h
Time and Distance question 5 of 28+Show Answer & Explanation
Answer: C. 80 km/h
Explanation: Required speed = 200/2.5 = 80 km/h.
Q6.A man reaches his office 10 minutes early at 15 km/h and 5 minutes late at 10 km/h. The distance to his office is:
Difficult- A6 km
- B7.5 km
- C8 km
- D9 km
Time and Distance question 6 of 28+Show Answer & Explanation
Answer: B. 7.5 km
Explanation: Time gap = 15 min = 1/4 h. d/10 − d/15 = 1/4 → d(3 − 2)/30 = 1/4 → d = 7.5 km.
Q7.Two cyclists start from the same point in the same direction at 12 km/h and 18 km/h. The gap between them after 3 hours is:
Easy- A12 km
- B15 km
- C18 km
- D20 km
Time and Distance question 7 of 28+Show Answer & Explanation
Answer: C. 18 km
Explanation: Relative speed = 18 − 12 = 6 km/h. Gap = 6 × 3 = 18 km.
Q8.A boy travels 24 km at 6 km/h and the next 24 km at 8 km/h. His average speed is:
Moderate- A6 6/7 km/h
- B7 km/h
- C7 1/2 km/h
- D8 km/h
Time and Distance question 8 of 28+Show Answer & Explanation
Answer: A. 6 6/7 km/h
Explanation: Time = 24/6 + 24/8 = 4 + 3 = 7 h for 48 km → average = 48/7 = 6 6/7 km/h.
Q9.A man covers half of his journey at 20 km/h and the remaining half at 30 km/h. His average speed is:
Easy- A24 km/h
- B25 km/h
- C26 km/h
- D28 km/h
Time and Distance question 9 of 28+Show Answer & Explanation
Answer: A. 24 km/h
Explanation: Equal halves → 2 × 20 × 30/(20 + 30) = 1200/50 = 24 km/h.
Q10.A speed of 5 m/s expressed in km/h is:
Easy- A15 km/h
- B16 km/h
- C18 km/h
- D20 km/h
Time and Distance question 10 of 28+Show Answer & Explanation
Answer: C. 18 km/h
Explanation: 5 × 18/5 = 18 km/h.
Q11.A man covers 60 km in 5 hours. His speed is:
Easy- A10 km/h
- B12 km/h
- C15 km/h
- D20 km/h
Time and Distance question 11 of 28+Show Answer & Explanation
Answer: B. 12 km/h
Explanation: Speed = 60/5 = 12 km/h.
Q12.A speed of 90 km/h expressed in m/s is:
Easy- A20 m/s
- B25 m/s
- C30 m/s
- D32 m/s
Time and Distance question 12 of 28+Show Answer & Explanation
Answer: B. 25 m/s
Explanation: 90 × 5/18 = 25 m/s.
Q13.A cyclist covers 20 km at 10 km/h and the next 20 km at 20 km/h. His average speed is approximately:
Moderate- A12.5 km/h
- B13.3 km/h
- C15 km/h
- D16.7 km/h
Time and Distance question 13 of 28+Show Answer & Explanation
Answer: B. 13.3 km/h
Explanation: Equal distances → 2uv/(u+v) = 2 × 10 × 20/30 = 400/30 ≈ 13.3 km/h.
Q14.A train covers 60 km in 45 minutes. Its speed is:
Easy- A70 km/h
- B75 km/h
- C80 km/h
- D90 km/h
Time and Distance question 14 of 28+Show Answer & Explanation
Answer: C. 80 km/h
Explanation: 45 min = 0.75 h → 60/0.75 = 80 km/h.
Q15.Walking at 5/6 of his usual speed, a man is 10 minutes late. His usual time is:
Moderate- A40 min
- B45 min
- C50 min
- D60 min
Time and Distance question 15 of 28+Show Answer & Explanation
Answer: C. 50 min
Explanation: Speed × 5/6 → time × 6/5. Extra time = 1/5 of usual = 10 min, so usual time = 50 minutes.
Q16.Two trains leave the same station in opposite directions at 40 km/h and 50 km/h. How far apart are they after 3 hours?
Easy- A150 km
- B210 km
- C240 km
- D270 km
Time and Distance question 16 of 28+Show Answer & Explanation
Answer: D. 270 km
Explanation: Combined separation rate = 40 + 50 = 90 km/h → 90 × 3 = 270 km.
Q17.A man walking at 4 km/h covers a distance in 2 hours 30 minutes. At 5 km/h he would take:
Easy- A1 h 40 min
- B2 hours
- C2 h 15 min
- D2 h 30 min
Time and Distance question 17 of 28+Show Answer & Explanation
Answer: B. 2 hours
Explanation: Distance = 4 × 2.5 = 10 km. At 5 km/h: 10/5 = 2 hours.
Q18.A car covers 300 km. If its speed were 10 km/h more, it would take 1 hour less. Its original speed is:
Difficult- A40 km/h
- B50 km/h
- C60 km/h
- D75 km/h
Time and Distance question 18 of 28+Show Answer & Explanation
Answer: B. 50 km/h
Explanation: 300/v − 300/(v + 10) = 1 → 3000 = v² + 10v → v² + 10v − 3000 = 0 → v = 50 km/h.
Q19.Sound travels at about 330 m/s. The distance it covers in 5 seconds is:
Easy- A1,320 m
- B1,500 m
- C1,650 m
- D1,800 m
Time and Distance question 19 of 28+Show Answer & Explanation
Answer: C. 1,650 m
Explanation: 330 × 5 = 1,650 metres.
Q20.A car travels the first 100 km at 50 km/h and the next 100 km at 25 km/h. Its average speed is:
Moderate- A30 km/h
- B33 1/3 km/h
- C37.5 km/h
- D40 km/h
Time and Distance question 20 of 28+Show Answer & Explanation
Answer: B. 33 1/3 km/h
Explanation: Time = 2 + 4 = 6 hours for 200 km → 200/6 = 33⅓ km/h.
Q21.A bus covers 120 km in 2 hours. Its speed is:
Easy- A50 km/h
- B60 km/h
- C70 km/h
- D80 km/h
Time and Distance question 21 of 28+Show Answer & Explanation
Answer: B. 60 km/h
Explanation: 120/2 = 60 km/h.
Q22.A speed of 72 km/h expressed in m/s is:
Easy- A15 m/s
- B18 m/s
- C20 m/s
- D25 m/s
Time and Distance question 22 of 28+Show Answer & Explanation
Answer: C. 20 m/s
Explanation: 72 × 5/18 = 20 m/s.
Q23.A runner covers 100 m in 10 seconds. His speed in km/h is:
Easy- A30 km/h
- B36 km/h
- C40 km/h
- D45 km/h
Time and Distance question 23 of 28+Show Answer & Explanation
Answer: B. 36 km/h
Explanation: 10 m/s = 10 × 18/5 = 36 km/h.
Q24.A man goes at 30 km/h and returns at 60 km/h along the same route. His average speed is:
Moderate- A40 km/h
- B45 km/h
- C48 km/h
- D50 km/h
Time and Distance question 24 of 28+Show Answer & Explanation
Answer: A. 40 km/h
Explanation: Equal distances → 2 × 30 × 60/90 = 3600/90 = 40 km/h.
Q25.A car travels 150 km at 50 km/h and the next 150 km at 30 km/h. Its average speed is:
Moderate- A35 km/h
- B37.5 km/h
- C40 km/h
- D42.5 km/h
Time and Distance question 25 of 28+Show Answer & Explanation
Answer: B. 37.5 km/h
Explanation: Time = 3 + 5 = 8 hours for 300 km → 300/8 = 37.5 km/h.
Q26.How long does a car take to cover 180 km at 60 km/h?
Easy- A2 hours
- B2.5 hours
- C3 hours
- D3.5 hours
Time and Distance question 26 of 28+Show Answer & Explanation
Answer: C. 3 hours
Explanation: 180/60 = 3 hours.
Q27.A speed of 25 m/s expressed in km/h is:
Easy- A75 km/h
- B80 km/h
- C90 km/h
- D100 km/h
Time and Distance question 27 of 28+Show Answer & Explanation
Answer: C. 90 km/h
Explanation: 25 × 18/5 = 90 km/h.
Q28.Two buses start towards each other from points 300 km apart at 40 km/h and 60 km/h. They meet after:
Moderate- A2 hours
- B3 hours
- C4 hours
- D5 hours
Time and Distance question 28 of 28+Show Answer & Explanation
Answer: B. 3 hours
Explanation: Closing speed = 100 km/h → 300/100 = 3 hours.
Time and Distance — Frequently Asked Questions
When do I use 2uv/(u+v) instead of the simple average?+
Use 2uv/(u+v) when the two speeds are used for equal DISTANCES (e.g. going and returning on the same route). Use the plain average only when the two speeds are used for equal TIMES.
What is the fastest way to handle "late by t minutes" problems?+
Write both journey times as distance/speed, set their difference equal to the total time gap in hours, and solve for distance. Or use the ratio method: if speed becomes a/b of usual, time becomes b/a of usual.
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