Quadratic Equations (C10)

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/hour more. Find the original speed of the train.

Answer

Let original speed of the train be x km/h.

Time taken at original speed = 360/x hours

Time taken at increased speed = 360/(x+5) hours

Now, 360/x - 360/(x+5) = 48/60

360[1/x - 1/(x+5)] = 4/5

x2 + 5x – 2250 = 0

x = 45 or –50

As speed cannot be negative

x = 45 km/h