A train travels 360 km at a uniform speed

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 = $\frac{D}{S}$

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

$T_1 = \frac{360}{x}$

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

$T_2 = \frac{360}{x + 5}$

by given condition, $T_2 = T_1 - 1$

$\therefore \frac{360}{x + 5}= \frac{360}{x} - 1$

$\therefore \frac{360}{x + 5}= \frac{360 - x}{x}$

$\therefore 360 x = (360 - x) (x + 5)$

$\therefore 360 x = 360 x - x^2 + 1800 - 5 x$

$\therefore x^2 + 5 x - 1800 = 0$

$\therefore x^2 + 45 x - 40 x - 1800 = 0$

$\therefore x (x + 45) - 40 (x + 45) = 0$

$\therefore (x + 45) (x - 40) = 0$

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 $\frac{360}{40} = 9$ hrs.

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

here, new time will be $\frac{360}{45} = 8$ hrs

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

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