Question

A plane left 30 minutes later than the scheduled time and in order to reach its destination 1500 km away on time, it has to increase its speed by 250 km/hr from its usual speed. Find the usual speed of the plane.

Answer 1

Let the usual speed of the plane be x km/hr
And the new speed of the plane after increased by 250 is `(x + 250)` km/hr
According to question

`1500/x - 1500/((x + 250)) = 30/60`

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

⇒ `1500 xx 250 xx 2 = x(x + 250)`

⇒ `750000 = x^2 + 250x`

⇒ `x^2 + 1000x - 750x - 750000 = 0`

⇒ `(x + 1000)(x - 750) = 0`

x = 750, - 1000

Speed can not be negative so -1000 will be neglected
Therefore, usual speed of the plane is 750 km/hr.