Question

A train covers a distance of 480 kilometre at a speed of x km/hr. If its speed is reduced to (x-20)km/hr, it takes 4 hr more to cover the same distance. Find the value of x

Answer 1

Original speed = 'x'km/hr
Distance = 480km
Therefore time taken = Distance/Speed = 480/x hours

New speed = (x-20)km/hr
Distance = 480km
Therefore, new time taken = 480/(x-20) hours

As per question, it takes 4 hours less if speed is reduced.
Therefore,
=> 4 = 480/+(x-20) - 480/x
=> 1 = 120/(x-20) - 120/x (dividing equation by 4)
=> 1 = 120x-120(x-20)/x(x-20)
=> x(x-20) = 120x-120x+2400
=> x^2-20x = 2400
=> x^2-20x-2400 = 0
=> x^2-60x+40x-2400 = 0
=> x(x-60)+40(x-60) = 0
=> (x+40)(x-60) = 0
=> x = -40 or 60
discarding -ve value as speed cannot be negative
=> x = 60km/hr