Q. A train travels 360 km at a uniform speed. If the seed had been 5 km/h more, it would have taken 1 jour less for the same journey. Find the speed of the train.

Ans:  Let take the speed of the train be x km/h.

We know that the time ‘T’ taken to cover a distance ‘D’ by an object moving at a speed ‘S’ is given by:

T =

Hence, Time taken to cover distance 360 km at a speed of x km/h will be:

Next, if Speed becomes (x + 5) km/h, Time taken will be:

by given condition,

∴  360 x = (360 – x) (x + 5)

∴ 360 x = 360 x – x² + 1800 – 5 x

∴ x² + 5 x – 1800 = 0

∴ x² + 45 x –  40 x – 1800 = 0

∴ x (x  + 45)  – 40 (x + 45) = 0

∴ (x  + 45) (x – 40) = 0

Therefore, x = – 45 and x = 40

Here, we reject x = – 45 because speed can not be negative.

Only x = 40 is accepted.

Hence, speed of the train is 40 km/h.

Check:

If speed is 40 km/h, it will take hrs.

When speed is increased by 5 km/h, new speed is 45 km/h,

here, new time will be hrs

Since this is 1 hr less than earlier time, hence our answer is correct.

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