Question

A man travels 300 km partly by train and partly by car. He takes 4 hours if he travels
60 km by train and the rest by car. If he travels 100 km by train and the remaining by
car, he takes 10 minutes longer. Find the speeds of the train and the car separately.​

Answer 1

Answer:

let the time taken by train be X and the time taken by car be Y

1st condition

60/X+240/Y =4 ( distance /speed=time)

2nd condition

100 /X +200/Y = 4+10/60

100/X +200/Y =25/6

now, let 1/X be U and 1 / Y be V

60U+ 240 V =4.........(I)

100 U +200 V= 25/6.......(.ii)

by by by by by

on solving x and y we get ,

X = 60 and Y = 80

hence , the speed of train is 60 km/h and the speed of car is 80 km/h

Answer 2

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$\bf{https://brainly.in/question/37581179}$

Let the speed of train and bus be u km/h and v km/h respectively.

According to the question,

$\frac{60}{u} + \frac{240}{v} = 4$....(i)

$\frac{100}{u} + \frac{200}{v} = 4 + \frac{10}{60} = \frac{25}{6}$....(ii)

Let $\frac{1}{u} = p\: and \frac{1}{v} = q$

The given equations reduce to:

60p + 240q = 4 ....(iii)

100p + 200q = $\frac{25}{6}$

600p + 1200q = 25....(iv)

Multiplying equation (iii) by 10, we obtain:

600p + 2400q = 40....(v)

Subtracting equation (iv) from equation (v), we obtain:

1200q = 15

q = $\frac{15}{1200} = \frac{1}{80}$

Substituting the value of q in equation (iii), we obtain:

60p + 3 = 4

60p = 1

p = $\frac{1}{60}$

:. p = $\frac{1}{u} = \frac{1}{60}$, q = $\frac{1}{v} = \frac{1}{80}$

u = 60 km/h , v = 80 km/h

Thus, the speed of train and the speed of bus are 60 km/h and 80 km/h respectively.

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