Question

a train travels 360akm at a uniform speed. if the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. find the speed of the train

Answer 1

Let the speed of the train initially be x km/h

so, as time = distance/speed

so, time = 360/x hr

Now, speed is increased by 5 km/h

so, new speed = x + 5 km/h

new time = 360 /(x+5)

According to question ;

360/x - 1 = 360/(x+5)

or, (360-x)/x = 360/(x+5)

or, (360-x)(x+5) = 360x

or, 360x + 1800 -x^2 -5x = 360x

or, x^2 + 5x - 1800 = 0

or, x = { -5 +- √(25 - 4×-1800) }/ 2

or, x = { -5 +- √(25+7200) }/2

or, x = ( -5 +- 85 )/2

or, x = 80/2 = 40 km/h ; x = -90/2 = -45 km/h(neglected )

so, the speed will be 40 kmph.