Question

ncert
A train travels a distance of 480 km at a uniform speed if the speed had been 8 km/hr less that it would have taken 3 hour more to cover the same distance we need to find the speed of the train

Answer 1

Let the speed of the train be x be km/hr

Given, Distance traveled by train = 480 km

Time is taken for the journey = 480/x   ---------- (1)

Given, speed is decreased by 8 km/hr

Time is taken for the journey = 480/(x-8)       -------- (2)

Given, it takes 3 hours more to cover distance    ------------- (3)

On solving(1),(2),(3), we get

480/x-8  - 480/x = 3

480x - 480(x-8) /x(x-8) = 3

48-(x-x+8)/x(x-8) = 3

1280 = x^2 - 8x

x^2 - 8x - 1280 = 0

x^2 - 40x + 32x - 1280 = 0 

x(x-40) + 32(x-40) = 0

(x+32)(x-40) = 0

x = -32 or x = 40.

the value cannot be negative.

The speed of the train = 40km/hr.