Question

Naveen travels 600 km to his home partly by train and partly by car. He takes 8 hours, if
he travels 120 km by train and the rest by car. He takes 20 minutes longer, if he travels 200 km by train and the rest by car. Find the speed of the train and the car.​

Answer 1

Answer:

$\huge\bf\purple{❥Question..!}$

Naveen travels 600 km to his home partly by train and partly by car. He takes 8 hours, if

he travels 120 km by train and the rest by car. He takes 20 minutes longer, if he travels 200 km by train and the rest by car. Find the speed of the train and the car.

$\huge\bf\purple{❥Answer..!}$

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

Case I: When he travels 120 km by train and the rest by car.

If Naveen travels 120km by train, then

Distance covered by car is (600−120)km=480km.

Now time taken to cover 129 km by train =120/x hrs[since Time=distance/speed]

time taken to cover 480 km by car=480/y hrs

it is given that total journey of the train is 8 hrs

∴120/x+480/y=8

$8( \frac{15}{x} + \frac{60}{y} ) = 8 \\ ( \frac{15}{x} + \frac{60}{y} ) = 1 \\ ( \frac{15}{x} + \frac{60}{y} ) - 1 = 0$

case ll: When he travels 200 km by train and the rest by car

If Naveen travels 200km by train, then

Distance travelled by car is (600−200)km=400km

Now, Time taken to cover 200km by train =

200/xhrs

Time taken to cover 400 km by train = 400/y hrs

In this case the total time of journey is 8 hour 20 minutes.

$\\\frac{200}{x} + \frac{400}{y} = 8hours20minutes\\ \frac{200}{x} + \frac{400}{y} = 8 \times \frac{1}{3 } \\ ⇒25( \frac{8}{x} + \frac{16}{y} ) = \frac{25}{3} \\ ⇒ \frac{8}{x} + \frac{16}{y} = \frac{1}{3} \\ ⇒ \frac{24}{x} + \frac{48}{y} = 1 \\ ⇒ \frac{24}{x} + \frac{48}{y} - 1 = 0$

now,Putting

1/x =u and

1/y =v in equations (i) and (ii), we get

15u+60v−1=0 (iii)

24u+48v−1=0 ..(iv)

by calculating we can get Hence, the speed of a train is 60 km/hr and the speed of a car is 80 km/hr.