Q. 164.4( 7 Votes )

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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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