Question

A passenger , while boarding the plane , slipped from the stairs and got hurt . The pilot took the passenger in the emergency clinic at the airport for treatment . Due to this, plane got delayed by half an hour . To reach the destination 1500 km away in time , so that the passengers could catch the connecting flight , the speed of the plane was increased by 250 km/hour than the usual speed . What is the usual speed of the plane ?

Answer 1

Answer:

Step-by-step explanation:

Solution :-

Let the usual speed of plane be x km/h.

Time taken as per usual speed = 1500/x hr

Time taken when speed is increased speed = (1500/x + 250)hr

According to the Question,

⇒ 1500/x - 1500/x + 250 = 1/2

⇒ {1500(x + 250) - 1500x/x(x + 250) = 1/2

⇒ 1500x + 375000 - 1500x = (x² + 250x)/2

⇒ x² + 250x - 750000 = 0

⇒ x² + 1000x - 750x - 750000 = 0

⇒ x(x + 1000) - 750(x + 1000) = 0

⇒ (x + 1000) (x - 750) = 0

⇒ x = - 1000, 750 (As speed cannot be negative)

⇒ x = 750

Hence, the usual speed of the plane is 750 km/ hr.