Question

a man travels 370 km partly by train and remaining by car. If He cover 250 km by train and the rest by the 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 train and that of car.

Answer 1

Linear Algebra: 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. What is the speed of the train and the car?

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Anurag Ahuja, foodie guy in this pay-for world :D

Answered Dec 10, 2016

Let the speed of the train be 'x' and that of the car be 'y'.

Hence, 250/x + 120/y = 4 ……(1)

Also, 130/x + 240/y = 4.3……..(2) (as 18 minutes of 60 is 0.3 of 1)

substitute 1/x = u and 1/y = v

Hence eq. 1 becomes, 250u +120v = 4 ……….(3)

Also, eq. 2 becomes, 130u + 240v = 4.3……….(4)

Multiplying eq. 3 by 2 and then subtracting it from eq. 4,

130u + 240v = 4.3

-500u - 240v = -8

Now, we get: -370u = - 3.7

370u = 3.7

Hence u = 3.7/370 = 0.01

Sub value of u in eq 3,

250(0.01) + 120v = 4

2.5 + 120v = 4

v = 1.5/120

v = 0.0125

Now, 1/x = u. Hence, x = 1/u

Similarly, y = 1/v

x = 1/0.01 = 100 kmph

y = 1/0.0125 = 80 kmph