Question

If the speed of an aeroplane is decreased by 120km/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 the distance?​

Answer 1

Step-by-step explanation:

Let average speed be V

Now V=s/t

Then according to given information,

1. V-120=s/(t+18/60)

2. V+180=s/(t-18/60)

Solving the above two equations for s

s=(V-120)(t+0.3)=(V+180)(t-0.3)=

Vt + 0.3V - 120t - 36 = Vt - 0.3V + 180t - 54

Shifting same variables to same side and solving further,

0.6V + 18 = 300t

Or

t = (0.6V + 18)/300

V = s/t = s/(0.6V + 18)/300 = 300s/(0.6V + 18)

Similarly, value of s can be calculated in terms of V using above equations. Once that is done, the resulting equation can be solved to obtain the value of V