Question

The time taken by Ram to cover 150 km in one direction was 150 minutes more than the time in the return journey. If he returned at a speed of 10 km/h more than the speed of onward journey, then find the speed of Ram in each direction​

Answer 1

here is your anwer.... i hope it helps

Answer 2

Given :

The time taken by Ram to cover 150 km in one direction was 150 minutes more than the time in the return journey.

To find :

If he returned at a speed of 10 km/h more than the speed of onward journey, then find the speed of Ram in each direction​

Solution:

Distance covered in one direction = 150 km

Let the speed of onward journey be x

$Time = \frac{Distance}{Speed}\\Time = \frac{150}{x}$

He returned at a speed of 10 km/h more than the speed of onward journey

Speed on returning =x+10

$Time = \frac{Distance}{Time}=\frac{150}{x+10}$

The time taken by Ram to cover 150 km in one direction was 150 minutes more than the time in the return journey.

$\frac{150}{x}-\frac{150}{x+10}=\frac{150}{60}\\ \frac{1}{x}-\frac{1}{x+10}=\frac{1}{60}\\\frac{10}{x(x+10)}=\frac{1}{60}\\600=x^2+10x\\x^2+30x-20x-600=0\\x(x+30)-20(x+30)=0\\(x-20)(x+30)=0\\x=20,-30$

Since the speed cannot be negative

So, speed on going = 20 km/h

Speed on returning = x+10=20+10=30 km/hr

Hence the speed of Ram on going is 20 km/hr and on returning is 30 km/hr