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Question

Places A and B are 80 km apart from each other on a highway. A car starts from A and other from B at the same time. If they move in the same direction they meet in 8 hours and if they move towards each other they meet in 1 hour and 20 minutes. Find the speeds of the cars.

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Solution

Let the speed of car starting from A=x km/hr and speed of car starting from B=y km/hr.

The relative speed of A with respect to B when moving in the same direction =xy km/hr.

The relative speed of A with respect to B when moving in opposite direction =x+y km/hr.

Distance between A and B=80 km.

We know, Time=DistanceSpeed

From the above information, we have,

80xy=8and80x+y=1+2060=43

or,80xy=8

10=xy

xy=10....(i)

Also,80x+y=43

240=4(x+y)

x=60y....(ii)

Substituting (ii) in (i), we get,

xy=10

60yy=10

602y=10

2y=50

y=25

Substituting y=25 in equation (ii), we get,

x=60y

x=6025

x=35

Thus, the speed of car starting from A=x=35 km/hr and speed of car starting from B=y=25 km/hr.

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