Question

A train takes 2 hours less for a journey of 200km if its speed increased by 5 km/hr from its usual speed.find its usual speed

Answer 1

let the usual speed of train be'x km / hr'

Given ,total distance = 200km ,

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Find usual time that it takes to cover the distance of 200 km :
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Time taken = distance / usual speed

Time taken = ( 200 / x ) hr ( usual )

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Find new time that it takes to cover the distance of 200 km :
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since ,the distance is same and the speed of train is increased by 5 km / hr

then , new speed = (usual speed + 5)

= ( x + 5 ) km / hr

Time taken = distance / new speed

= 200 / (x + 5 ) hr ( new )

according to question ,
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in simple way: a train takes 2 hr less from its usual time when its speed increased by 5 km/hr
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usual time - 2 = new time

( 200/ x ) - 2 = 200 / ( x + 5 )

( 200 - 2 x ) / x = 200 / ( x + 5 )

(x + 5 ) (200 - 2 x ) = 200 x

200 x - 2 x^2 + 1000 - 10 x = 200 x

- 2 x^2 - 10 x + 1000 = 200x - 200 x

- 2 ( x^2 + 5 x - 500 ) = 0

x^2 + 5 x - 500 = 0

x^2 + 25 x - 20 x - 500 = 0

x ( x + 25 ) - 20 ( x + 25 ) = 0

(x - 20 ) ( x + 25 ) = 0

x - 20 = 0 , x + 25 = 0

x = 20 , x = - 25 ( neglect it )

speed can not be -ve so neglect (- 25 ).

take positive value x = 20 km / hr

therefore ,

usual speed of train = 20 km / hr

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Your Answer : usual speed = 20 km / hr
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Answer 2

Answer:

Let the usual speed of the train be y km / hr .

A.T.Q.

$\displaystyle{\frac{300}{y} -\frac{300}{y+5} =2 }$

300 ( y + 5 ) - 300 y = 2 y ( y + 5 )

y² + 5 y - 750 = 0

y² + 30 y - 25 y - 750 = 0

( y + 30 ( y -25 ) = 0

y = - 30 or y = 25

Since , speed of train can't be negative .

Therefore , the usual speed of the train is 25 km / hr .