Question

The train covers a distance of 600km at 6km/hr . Had the speed been (x+20)km/hr more , the time taken to cover the distance would have been reduced by 5 hours . Find x .

Answer 1

Time required to cover 600 km at x km/hr = 600/x hours

Time required to cover 600 km at (x + 20) km/hr = 600/(x + 20) hours

As per problem, 600/x – 600/(x + 20) = 5

Or, [600(x +20) – 600x]/x(x +20) = 5

Or, [600x + 12000 – 600x]/(x² + 20x) = 5

Or, 12000/(x² + 20x) = 5

Or, x² + 20x = 2400

Or, x² + 20x – 2400 = 0 [

Or, x² + (60 – 40)x – 2400 = 0

Or, x² + 60x – 40x – 2400 = 0

Or, x(x + 60) – 40(x + 60) = 0

Or, (x + 60)(x – 40) = 0

Either, x + 60 = 0 Or, x – 40 = 0

Either x = – 60 Or, x = 40

Neglecting x = – 60, as negative speed is never possible, x = 40 km/hr. [Ans.]