While boarding an aeroplane, a passenger got hurt. The pilot showing promptness and concern, made arrangements to hospitalize the injured and so the plane started late by 30 minutes to reach the destination, 1500 km away in time, the pilot increased the speed by 100 km / hr. Find the original speed / hour of the plane.

Given: Increment in speed = 100 km/h

Distance = 1500 km

To find: The original speed

Method Used:

To solve the quadratic equation by factorisation method, follow the steps:

1) Multiply the coefficient of x2 and constant term.

2) factorise the result obtained in step 1.

3) Now choose the pair of factors in such a way that after adding or subtracting(splitting) them

You get coefficient of x.

Explanation:

Given, while boarding an aeroplane, a passenger got hurt and the plane started late by 30 minutes to reach the destination, 1500 km away in time, the pilot increased the speed by 100km/hr.

Let the usual speed be ‘a’.

⇒ 2 × 1500 × (a + 100 –a) = a² + 100a

⇒ a² + 100a – 300000 = 0

⇒ a² + 600a – 500a – 300000 = 0

⇒ a (a + 600) – 500(a + 600) = 0

⇒ (a + 750) (a – 500) = 0

⇒ a = 500 km/hr.

Hence the usual speed is 500 km/hr.