Question

If the speed of an aeroplaneis decreased by 120 km/hr, it takes 18 minutes more to travel some distance. If the speed is increased by 180 km/hr,it takes 18 minutes less to travel the same distance. Find the average speed of the aeroplane and tge distance.

Answer 1

Let its average speed = x km/hr and distance = y km.

We have two conditions here.

Condition 1 :

If the speed of an aeroplane is decreased by 120 km/h, it takes 18 minutes more  to travel some distance.

=> (y/x - 120) - y/x = 18/60

=>  y * [1/(x - 120) - 1/x] = 18/60

Condition 2 :

If the speed is increased by 180 km/h, it takes 18 minutes  less to travel the same distance.

=> (y/x) - (y/x + 180) ] = 18/60

=> y * [1/x - 1/x + 180] = 18/60

Solve 1 and 2 conditions, we will get

=> (1/x - 120) - 1/x = 1/x - 1/x + 180

=> 120(x + 180) = 180(x - 120)

=> x = 720 km/hr

Place x in condition (1).

=> y * (1/(720 - 120) - 1/720] = 18/60

=> y[1/600 - 1/720] = 18/60

=> y = 1080 km

Hence,

Average Speed = 720 km/hr and Distance = 1080 km.

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