A man left town M at 10:00a.m. and travelled by car to town N at an average speed of 72km/h. He spent 2hours for a meeting and returned to town M by bus at an average speed of 40km/h. If the distance covered by the bus was 2km longer than that of the car and he arrived at town M at 1:55pm. Calculate the distance from M to N.

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Adetunmbiadekunle Adetunmbiadekunle · Answer 1 · 2021-09-22T15:00:51+02:00

Distance from M to N = 48.24 km

The car speed = 72 km/h

Time spent by the car = t

Time spent for the meeting = 2 hours

Total time spent since the man left town M till when he returns = 1:55pm - 10:00am = 3 hrs 55 minutes = 3.92 hours

Distance from M to N = Speed of the car * Time spent by car

Distance from M to N = 72 x t

Distance from M to N = 72 t

The man traveled by bus back to town M from town N

If the distance from N to M is 2 km longer than the distance from M to N, it means the car and the bus passed through different routes

Distance from N to M = (Distance from M to N) + 2..................(*)

Time taken by the bus = (Total time) - (Time taken by car) - (Time spent for the meeting)

Time taken by the bus = 3.92 - t - 2

Time taken by the bus = 1.92 - t

Distance from N to M = Speed of the bus x Time taken by the bus

Distance from N to M = 40 x (1.92 - t)...................(**)

Substitute (*) into (**)

(Distance from M to N) + 2 = 40 x (1.92 - t)

72t + 2 = 40(1.92 - t)

72t + 2 = 76.8 - 40t

72t + 40t = 76.8 - 2

112t = 74.8

t = 74.8/112

t = 0.67 hours

Distance from M to N = 72t

Distance from M to N = 72(0.67)

Distance from M to N = 48.24 km

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