Question

A train covers a distance of 90 km at a uniform speed. Had the speed been 15 km/hour more, it would have taken 30 minutes less for a journey. Find the original speed of the train.

A train covers a distance of 90 km at a uniform speed. Had the speed been 15 km/h more, it would have taken 30 minutes less for the same journey. Find the original speed of the train.

Answer 1

Let the original speed of train be x km/hr.

Then, Increased speed of the train = (x + 15) km/hr

Time taken by the train under usual speed to cover 90 km = `90/x`hr

Time taken by the train under increased speed to cover 90 km = `90/(x + 15)`hr

Therefore,

`90/x - 90/(x + 15) = 30/60`

`(90(x + 15) - 90x)/(x(x + 15)) = 1/2`

`(90x + 1350 - 90x)/(x^2 + 15x) = 1/2`

`1350/(x^2 + 15x) = 1/2`

1350(2) = x² + 15x

2700 = x² + 15x

x² + 15x – 2700 = 0

x² – 45x + 60x – 2700 = 0

x(x – 45) + 60(x – 45) = 0

(x – 45)(x + 60) = 0

So, either 

x – 45 = 0

x = 45

Or

x + 60 = 0

x = –60

But, the speed of the train can never be negative.

Hence, the original speed of train is x = 45 km/hr