Question

A passenger train leaves Town A at 10 40 and travels at 80 km/h to Town B, arriving there at 13 25.
Find the distance between Town A and Town B.

Answer 1

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Answer 2

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Let the speed of the average passenger train be 'x' km/hr.

So, the time taken by the passenger train = 192/x.

So, the average speed of the super fast train = (x + 16) km/hr

So, the time taken by the super fast train = 192/(x + 16).

Given : Time taken by the passenger train to travel 192 km - time taken by super fast train to cover the distance of 192 km = 2 hours.

Therefore,

192/x - 192/(x + 16) = 2 Taking L.C.M.. we get

(192x + 3072 + 192x)/(x)(x+16) = 2

3072/x(x + 16) = 2 After cross multiplying, we get

3072 = 2x² + 32x

2x² + 32x - 3072 = 0

Dividing it by 2, we get

x² + 16x - 1536 = 0

x² + 48x - 32x - 1536 = 0

x(x + 48) - 32(x + 48) = 0

(x + 48) (x - 32) = 0

x = - 48 or x = 32

The speed of the train cannot be negative, therefore the speed of the passenger train is 32 km/hr

And the speed of the super fast train is 32 + 16 = 48 km/hr

$\huge\underline\mathcal\purple{EXO}$