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

Ans:

Let’s consider the speed of the train is X km/hr.

Now, to cover distance of 360 km, it will take \frac{360}{\times} hrs

Next, we are given that if speed is increased by 5 km/hr, then new speed will be: (X + 5) km/hr

Now, with this new speed, time taken to cover distance of 360 km, it will take \frac{360}{\times + 5} hrs

Given that, new time is 1 hr less than the present time.

\therefore \frac{360}{\times + 5} = \frac{360}{\times} - 1

\therefore \frac{360}{\times + 5} = \frac{360 - \times}{\times}

\therefore 360 \times = (360 - X) ( X + 5)

\therefore 360 \times = 355 \times - \times^2 + 1800

\therefore \times^2 + 5\times - 1800 = 0

\therefore (\times + 45) ( \times - 40) = 0

\therefore \times = - 45, \times = 40

Since, the speed can not be negative, hence X = 40

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

Check: At 40 kmph, train will take 9 hrs to cover 360 km. At 5 kmph higher speed i.e. at 45 kmph, train will take 8 hrs, which is 1 hr less. Hence, X = 40 kmph is correct.

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