A passenger train takes one hour less for a journey of 150 km if its speed is increased by 5 km/hr from its usual speed. Find the usual speed of the train.

Given:

A passenger train takes one hour less for a journey of 150 km if its speed is increased by 5 km/hr from its usual speed.

To do:

We have to find the usual speed of the train.

 Solution:

Let the usual speed of the train be $x$ km/hr.

This implies,

Time taken by the train to travel 150 km at usual speed$=\frac{150}{x}$ hours

Time taken by the train to travel 150 km when the speed is 5 km/hr more than the usual speed$=\frac{150}{x+5}$ hours

According to the question,

$\frac{150}{x}-\frac{150}{x+5}=1$

$\frac{150(x+5)-150(x)}{(x)(x+5)}=1$

$\frac{150(x+5-x)}{x^2+5x}=1$

$150(5)=1(x^2+5x)$   (On cross multiplication)

$750=x^2+5x$

$x^2+5x-750=0$

Solving for $x$ by factorization method, we get,

$x^2+30x-25x-2250=0$

$x(x+30)-25(x+30)=0$

$(x+30)(x-25)=0$

$x+30=0$ or $x-25=0$

$x=-30$ or $x=25$

Speed cannot be negative. Therefore, the value of $x$ is $25$ km/hr.

The usual speed of the train is $25$ km/hr. 

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Updated on: 10-Oct-2022

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