Question

A man travels 370 km partly by train and partly by car. If he covers 250 km by train and the rest by car , he takes 4 hours . But , if he travels 130km by train and the rest by car he takes 18 minutes more. Find the speed of the train and car.

Answer 1

Let the speed of the train be t and the speed of the car be c.

250/t+ 120/c = 4, or

250 c + 120 t = 4 tc …(1)

130/t + 240/c = 4+18/60 = 4.3, or

130 c + 240 t = 4.3 tc …(2)

Multiply (1) by 2 to get

500 c + 240 t = 8 tc …(3)

Subtract (2) from (3),

500 c - 130 c = 8 tc - 4.3 tc, or

370 c = 3.7 tc, or

t = 100.

From (1): 250 c + 120 t = 4 tc, or

250 c + 120*100 = 4*100 c, or

400c - 250 c = 12000, or

150 c = 12000, or

c= 12000/150 = 80

So the speed of the train is 100 kmph and that of the car is 80 kmph.

Check: 250/100 + 120/80 = 2.5 + 1.5 = 4 hours. Correct.

130/100 + 240/80 = 1.3 + 3 = 4.3 hours or 4 hours and 18 mins. Correct.