#### Question

The speed of an ordinary train is x km per hr and that of an express train is (x + 25) km per hr.

(1) Find the time taken by each train to cover 300 km.

(2) If the ordinary train takes 2 hrs more than the express train;calculate speed of the express train.

#### Solution

1) Speed of ordinary train = x km/hr

Speed of express train = (x + 25) km/hr

Distance = 300 km

We know

`"Time" = "Distance"/"Speed"`

∴ Time taken by ordinary train to cover 300 km = `300/x` hrs

Time taken by express train to cover 300 km = `300/(x + 25)` hrs

2) Given that the ordinary train takes 2 hours more than the express train to cover the distance.

Therefore,

`300/x - 300/(x + 25) = 2`

`(300x + 7500 - 300x)/(x(x + 25)) = 2`

`7500 = 2x^2 + 50x`

`2x^2 + 50x - 7500 = 0`

`x^2 + 25x - 3750 = 0`

`x^2 + 75x - 50x - 3750 = 0`

x(x + 75) - 50(x + 75) = 0

(x + 75)(x - 50) = 0

x = -75, 50

But, speed cannot be negative. So, x = 50.

∴ Speed of the express train = (x + 25) km/hr = 75 km/hr