Answer :

**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) = a^{2} + 100a

⇒ a^{2} + 100a – 300000 = 0

⇒ a^{2} + 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**.

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