Time, Speed and Distance — Practice

Question 1

A speed of 54 km/h expressed in m/s is:
(a) 12 m/s (b) 15 m/s (c) 18 m/s (d) 20 m/s

Accepted Answer

(b) 15 m/s.

54 × 5/18 = 15. Worth memorising as an anchor along with 36→10, 72→20, 90→25.

Question 2

A man drives to town at 60 km/h and returns along the same road at 40 km/h. His average speed for the whole journey is:
(a) 50 km/h (b) 48 km/h (c) 45 km/h (d) 52 km/h

Accepted Answer

(b) 48 km/h.

Equal distances → harmonic mean: 2 × 60 × 40 / (60 + 40) = 4800/100 = 48. The tempting 50 ignores that the slower leg takes longer.

Question 3

A 150 m long train running at 54 km/h crosses an electric pole in:
(a) 8 s (b) 10 s (c) 12 s (d) 15 s

Accepted Answer

(b) 10 s.

Speed = 54 × 5/18 = 15 m/s. A pole has no length, so the train covers only its own 150 m: 150 ÷ 15 = 10 s.

Question 4

A 240 m long train running at 72 km/h crosses a 360 m long platform in:
(a) 18 s (b) 24 s (c) 30 s (d) 36 s

Accepted Answer

(c) 30 s.

Speed = 72 × 5/18 = 20 m/s. Distance = own length + platform = 240 + 360 = 600 m. Time = 600 ÷ 20 = 30 s.

Question 5

Two trains 120 m and 180 m long run at 42 km/h and 66 km/h towards each other. They will cross each other in:
(a) 8 s (b) 10 s (c) 12 s (d) 15 s

Accepted Answer

(b) 10 s.

Opposite directions → relative speed = 42 + 66 = 108 km/h = 30 m/s. Distance = 120 + 180 = 300 m. Time = 300 ÷ 30 = 10 s.

Question 6

A 100 m train at 72 km/h overtakes a 150 m train moving at 54 km/h in the same direction. The time taken to pass it completely is:
(a) 25 s (b) 40 s (c) 50 s (d) 60 s

Accepted Answer

(c) 50 s.

Same direction → relative speed = 72 − 54 = 18 km/h = 5 m/s. Distance = 100 + 150 = 250 m. Time = 250 ÷ 5 = 50 s.

Question 7

A boat travels at 10 km/h downstream and 6 km/h upstream. The speed of the stream is:
(a) 1 km/h (b) 2 km/h (c) 3 km/h (d) 4 km/h

Accepted Answer

(b) 2 km/h.

Stream = (downstream − upstream)/2 = (10 − 6)/2 = 2 km/h; boat in still water = (10 + 6)/2 = 8 km/h.

Question 8

Walking at ¾ of his usual speed, a man reaches office 10 minutes late. His usual time to reach office is:
(a) 20 min (b) 25 min (c) 30 min (d) 40 min

Accepted Answer

(c) 30 min.

At ¾ speed, time becomes 4/3 of usual — the extra ⅓ of the usual time is the 10-minute delay. So usual time = 30 min. No equations needed: time ratios invert speed ratios.

Question 9

Travelling at 40 km/h a person reaches 10 minutes late; at 50 km/h he reaches 5 minutes early. The distance of his destination is:
(a) 40 km (b) 50 km (c) 60 km (d) 80 km

Accepted Answer

(b) 50 km.

The time gap between the two speeds is 10 + 5 = 15 min = ¼ h. d/40 − d/50 = d/200 = ¼ → d = 50 km. Check: 75 min vs 60 min — exactly 15 minutes apart ✓.

Question 10

A policeman spots a thief 200 m away. The thief runs at 10 km/h and the policeman chases at 12 km/h. The thief is caught after:
(a) 5 min (b) 6 min (c) 8 min (d) 10 min

Accepted Answer

(b) 6 min.

Relative speed = 12 − 10 = 2 km/h; gap = 0.2 km. Time = 0.2 ÷ 2 = 0.1 h = 6 minutes. (In that time the thief runs a further 1 km.)

Practice — Time, Speed and Distance

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