Question

A faster train takes one hour less than a slower trade for a journey of 200 km if the speed of your train is 10 kilometre per hour less than the fastest and find the speed of two trains

Answer 1

isnt  the speed of the faster train 50km/h and the slower train 40km/h ?

Answer 2

Let the speed of the faster train = x km/h

Then the speed of the slower train = (x-10) km/h

Time taken by the faster train to travel 200km = $\sf{\frac{200}{x}h}$

Time taken by the slower train to travel 200km = $\sf{\frac{200}{x-10}h}$

A/C,

$\sf\red{\frac{200}{x - 10} - \frac{200}{x} = 1}$

$\longrightarrow$$\sf\red{200(x(x - 10)) = x(x - 10)}$

$\longrightarrow$$\sf\red{{x}^{2} - 10x - 2000 = 0}$

$\longrightarrow$$\sf\red{(x - 50)(x + 40) = 0}$

$\longrightarrow$$\sf\red{x = 50 \:or \: x = - 40}$

As the speed cannot be negative, x ≠-40 ,so x = 50

Hence, the speed of the faster train = 50km/h

And the speed of the slower train = 50 - 10 = 40km/h