Q. 164.4( 7 Votes )

# <span lang="EN-US

Answer :

Given: Increment in speed = 250 km/h

Distance = 1250 km

To find: Its usual 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, aeroplane left 50 minutes later than its schedule time,

and in order to reach the destination, 1250 km away, in time,

it had to increase its speed to 250 km / hr. from its usual speed.

Let the usual speed be ‘a’.

Increased speed = a + 25

As, So usual time is When speed is increased time will be As speed increases time decreases

So according to question,    6 × 1250 × (a + 250 –a) = 5(a2 + 250a)

a2 + 250a – 375000 = 0

a2 + 750a – 500a – 375000 = 0

a(a + 750) – 500(a + 750) = 0

(a + 750) (a – 500) = 0

a = 500 km/hr

Hence the usual speed is 500 km/hr.

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