A plane left 30 minutes later than the scheduled time and in order to reach its destination 1500 km away in time it has to increase its speed by 250 km/hr from its usual speed. Find its usual speed.
750 km/hr
Let the usual speed of the plane be x km/hr.
Then, time taken to cover 1500 km with the usual speed
=1500xhrs
Time taken to cover 1500 m with the speed of (x+250)km/hr=1500x+250
∴1500x=1500x+250+12
⇒1500x−1500x+250=12
⇒1500x+1500×250−1500xx(x+250)=12
⇒1500×250x2+250x=12
⇒750000=x2+250x
⇒x2+250x−750000=0
⇒x2+1000x−750x−750000=0
⇒x(x+1000)−750(x+1000)=0
⇒(x+1000)(x−750)=0
⇒x=−1000 or, x=750
⇒x=750
[∵ speed cannot be negative]
Hence, the usual speed of the plane is 750 km/hr