Question

36. Avinash travels a distance of 820 km partly by car and partly by train.

If he travels a distance of 700 km by car and rest by train then he takes 12

hours. But if he travels 350 km by car and the rest by train then he takes 50

minutes more. Find the speeds of the car and the train​

Answer 1

speed of the car =70km/hr

speed of the bus=60 km/hr.

Answer 2

The speed of the car and the train​ are 70 km/hr and 60 km/hr respectively.

Step-by-step explanation:

Gain:

A distance of 820 km is traveled by Avinash partly by car and partly by train.

Avinash travels a distance of 700 km by car and rest by train then he takes 12 hours.

Avinash 350 km by car and the rest by train then he takes 50 minutes more

To  Find:

The speed of the car and the train​.

Formula Used:

$Speed=\frac{Distance\ traveled}{Time\ taken\ to\ travel\ distance}$

Solution:

As given-a distance of 820 km is traveled by Avinash partly by car and partly by train.

Let the speed of the  car and  the train  is p  km/hr and q km/hr respectively.

As gievn - Avinash travels a distance of 700 km by car and rest by train then he takes 12 hours.

Time taken by Avinash to travel 700 km by car $=\frac{700}{p}$

Time taken by Avinash to travel $(820-700)=120$ by train $=\frac{120}{q}$

$\frac{700}{p} +\frac{120}{q} =12$

$\frac{175}{p} +\frac{30}{q} =3$   --------------- equation no.01.

As gievn - Avinash travels a distance of 350 km by car and rest by train then he takes 50 minutes more.

It means time taken is 12hours and 50 minutes $=(12+\frac{50}{60}) hours =\frac{770}{60} hours=\frac{77}{6} hours.$

Time taken by Avinash to travel 350 km by car $=\frac{350}{p}$

Time taken by Avinash to travel $(820-350)=470$ by train $=\frac{470}{q}$

$\frac{350}{p} +\frac{470}{q} =\frac{77}{6}$  ------------ equation no.2.

Multiplying the equation no. 01 by 2 and subtracting  from equation no.02. We get.

$\frac{470}{q} -\frac{60}{q} =\frac{77}{6} -6$

$\frac{410}{q} =\frac{77-36}{6}$

$\frac{410}{q} =\frac{41}{6}$

$q=60 \ km/hr$

Putting the value of q in equation no.01. We get.

$\frac{175}{p} +\frac{30}{60} =3$

$\frac{175}{p} +\frac{1}{2} =3$

$\frac{175}{p} =3-\frac{1}{2} =\frac{5}{2}$

$p=\frac{175\times2}{5} = 70\ km/hr$

Thus,the speed of the car and the train​ are 70 km/hr and  60 km/hr respectively.

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