Question

A man travels 600km partly by train and partly by car. h takes 8 hand 40 min, if he travels

320 km by train and the rest by car. It would take 30 min more, If he travels 200 km by train

and the rest by car. Find the speed of The train and the car separately.​

Answer 1

Answer:-

The speed of train = 80 km/hr.

The speed of car = 60 km/hr.

Explanation.

Let the speed of train = x

Let the speed of car = y

Total distance travelled = 600 km

The time taken by the man to travel 320 km

by train is = 320 / x

The time taken by the man to travel 280 km

by car is = 280 / y

Total time taken by a man to travel 600 km is

320 / x + 280 / y

Total time = 8 hours 40 minutes = 26 / 3 hours

Therefore,

$\frac{320}{x} + \frac{280}{y} = \frac{26}{3} \: \: .......(1)$

The time taken by a man to travel 200 km

by train = 200 / x

The time taken by a man to travel 400 km

by train = 400 / y

Total Time taken by a man to travel 600 km

$\frac{200}{x} + \frac{400}{y}$

Given,

time taken is 30 minutes more than

8 hours 40 minutes = 26 / 3 + 1/2 = 55 / 6 hrs

Therefore,

$\frac{200}{x} + \frac{400}{y} = \frac{55}{6} \: \: .....(2)$

substitute the value =

1/x = a and 1/y = b

Therefore,

equation will be written as =

320a + 280y = 26 / 3 ..... (1)

200a + 400y = 55 / 6 .... (2)

solving the equation we get,

a = 1/80

put the value of a = 1/80 in equation (1)

we get,

b = 1/60

Therefore,

1/x = a = 1/x = 1/80 = x = 80 km/hr

1/y = b = 1/y = 1/60 = y = 60 km/hr

Therefore,

speed of train = 80 km/hr

speed of car = 60 km/hr