Question

A plane left 30 minutes late than its scheduled time and in order to reach the destination 1500 km away in time it had to increase its speed by 100km/h from the usual speed. Find its usual speed..

Answer 1

Usual speed of plane = 500Km/h

Answer 2

Let the scheduled time be T hr.

Now we know that speed = distance/time. So,

Speed of aeroplane = Distance covered/ Time taken
= 1500/T  ........(1)
ATQ 

Time taken by Aeroplane = Scheduled time - 30 minutes 
= (T - 1/2) hour 

Now, Speed of aeroplane = 1500/(T - 1/2) .......(2)
ATQ
1500/(T - 1/2) - 1500/T = 100
1500 { (T - T + 1/2)/(T² - T/2) }= 10015×1/2 = T² - T/2 15 = 2T² - T 2T² - T - 15 = 0 2T² - 6T + 5T - 15 = 0 
2T ( T - 3) 5( T- 3) = 0T = 3 or -5/2
 T ≠ -5/2

So, T = 3 
Therefore usual speed of aeroplane = 1500/T = 1500/3 = 500 km/hr