<span lang="EN-US

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.