Question

A train, travelling at a uniform speed for 360 km, would have taken 48 minutes less to travel the same distance if its speed were 5 km/h more. Find the original speed of the train.

Answer 1

Let the speed of the train is x km/hr

Given, the train travelling at a uniform speed for 360 km would have taken 48 minutes less to travel the same distance

if its speed work 5 km per hour more.

=> 360/x - 360/(x + 5) = 48/60           {since 48 minutes = 48/60 hours}

=> 360{1/x - 1/(x + 5)} = 4/5

=> 360[{(x + 5) - x}/{x(x + 5)}] = 4/5

=> 360[{x + 5 - x}/{x(x + 5)}] = 4/5

=> 360[5/{x2 + 5x}] = 4/5

=> 1800/{x2 + 5x}] = 4/5

=> 1800*5 = 4(x2 + 5x)

=> (1800*5)/4 = x2 + 5x

=> x2 + 5x = 450*5

=> x2 + 5x = 2250

=> x2 + 5x - 2250 = 0

=> x2 - 45x + 50x - 2250 = 0

=> x(x - 45) + 50(x - 45) = 0

=> (x - 45)*(x + 50) = 0

=> x = 45, -50

Since speed can not be negative

So, x = 45

speed of the train is 45 km/h