Question

an aeroplane left 50 minutes later than its scheduled time and in order to reach the destination 1250 km away in time had to increase its speed by 250km/h from its usual time. find its usual time

Answer 1

Solution:-
There is a mistake in the question. Instead of usual time it should be usual speed.
Let the usual speed of the plane = 'x' km/hr
Increased speed of the plane = (x+250) km/hr
Time taken to reach the destination at usual speed T1 = 1250/x hr
Time taken to reach the destination at increased speed T2 = 1250/(x+250) hr
Given : T1 - T2 = 50 minutes.
∴ 1250/x hr - 1250/(x+250) hr = 50/60
After taking L.C.M of x and x+250 and then solving it, we get
(1250x + 312500 - 1250x)/x(x+250) = 5/6
312500 × 6 = 5(x²+250x)
1875000 = 5x² + 1250x 
dividing this by 5, we get
(1875000 = 5x² + 1250x)/5
375000 = x² + 250x
x² + 250x - 375000 
x² + 750x - 500x - 375000
x (x+750) - 500 (x+750)
(x-500) (x+750)
x =500 km/hr because x = -750 is not possible as speed cannot be negative.
So, the usual speed is 500 km/hr