Question

A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it
would have taken 3 hours more to cover the same distance. We need to find the speed of the train?​

Answer 1

let time taken=t

speed=480/t

again, time=t+3

speed=480\t+3

a/q, 480/t-480/t+3=8

by solving eq we get

t=12 h

so, uniform speed=480/12=40m/s

Answer 2

x=40 km/hour

Step-by-step explanation:

Let the speed of train be x km/hour

time taken to cover 480 km = $\frac{480}{x} hour$

according to question

$(x-8)(\frac{480}{x}+3)=480\\\frac{480x}{x}+3x-\frac{3840}{x}-24=480\\3x^2-3840-24x=0\\3x^2-24x-3840=0\\x^2-8x-1280=0\\(x^2-40x)+(32x-1280)\\x(x-40)+32(x-40)\\(x+32)(x-40)\\x=-32,x=40$

Speed cannot be negative

$\therefore$ the speed of train is 40 km/hour