On a journey of 600 km, a train was delayed 1 hour and 30 min after having covered 1 4 of the way. To arrive on time at the destination, the engine driver had to increase the speed by 15 km/hour. How long did the train travel for

The train travelled 10hours.

Explanation:

Using speed= distance/time ...eq1

Let the time taken by train to cover the journey be t.

Let the speed of train be s

Time= distance/speed ...eq2

Time t =600/s ...eq3

The train is delayed for 1 1/2 hours=3/2 hours

Train increased by 15km/hr.

Train travelled 1/4 of 600k.= 150km.

Speed increased by s + 15 to cover the remaining 450km

t = 150/s + 400/(s + 15) + 3/2 ..eq4

Equating eq3 and 4

600/s= 150/s + 460/(s + 15) + 3/2

450/s = 3/2 + 450/(s + 15)

3s^2 + 45s -13500=0

Solving the quadratic equation

S= -45 +-sqrt(45^2-4(3×13500)/2×3

S= 60 , -75

Hence speed of train is 60km/hr

Using eq 2 distance/speed=time

600/60=10

t= 10hours