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 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 hrs

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

∴ 360 X = (360 – X) ( X + 5)

∴ 360 X = 355 X – X² + 1800

∴ X² + 5 X – 1800 = 0

∴ (X + 45) (X – 40) = 0

∴ X  = – 45, X = 40

Since, the speed can not be negative, We reject X = – 45. hence X = 40

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

Check: At 40 kmph, train will cover 360 km in = 9 hrs.

By 5 kmph more, new speed is at 45 kmph, and train will take = 8 hrs,

Since new time is 1hr less than earlier – it matches the given condition. Hence, X = 40 kmph is correct.

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