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, it takes him 4 hours. But, if he travels 130 km by train and the rest by car, he takes 18 minutes longer. Find the speed of the train and that of the car.

Answer 1

Let the speed of a train = x km/hr

And the speed of a car = y km/hr

Total distance travelled = 370km

According to the question,

If he covers 250km by train and rest by car i.e. (370 – 250) = 120km

Time take = 4hrs

If he travels 130km by train and rest by car i.e. (370 – 130) = 240km

250u + 120v = 4 …(iii)

and 130u + 240v = 4.3 …(iv)

On multiplying Eq. (iii) by 2

500u + 240v = 8 …(v)

On subtracting Eq. (iv) from Eq. (v), we get

500u + 240v – 130u – 240v = 8 – 4.3

⇒ 370u = 3.7

⇒ x = 100 and y = 80

Hence, the speed of the train is 100km/hr and the speed of the car is 80km/hr.