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 130km by train and the rest by the car he takes 18 min. longer. Find the speed of the train and car.

Total distance = 370 km

Case 1

Distance covered by train = 250 km

Distance covered by car = total distance - distance traveled by train

= 370 – 250

= 120 km

Total time = 4 hours

Let the speed of train be x km/hr and the speed of car be y km/hr.

Total time taken = time taken for train’s journey + time taken for car's journey

…….(1)

Case 2

Distance covered by train = 130 km

Distance covered by car = Total distance – distance covered by train

= 320 – 130

= 240 km

Time = time taken in Case 1 + 18 minutes

= 4 hrs + 18 min

Converting 18 minute to hours

60 min = 1 hr

For 18 minutes

= 4.3 hrs

Let speed of train = x km/hr

The speed of car = y km/hr

Total time took = time taken for train's journey + time taken for car's journey

……(2)

Eliminate (1) and (2)

Let,

(250a + 120b = 4) ……multiply by 2

(130a + 240b = 4.3) ……multiply by 1

370a = 3.7

x = 100

y = 80

Therefore, the speed of the train is 100 km per hour and the speed of the car is 80 km per hour.