Question

The time taken by a person to cover 150 km was 2.5 hrs more than the time taken in the return journey. If he returned at a speed of 10 km / hr more than the speed of going, what was the speed per hour in each direction?

Answer 1

Time = distance/speed 

Let the speed of person on onward journey be ‘a’ km/hr Speed at which he returned = a – 10 km/hr 

Given, time taken by a person to cover 150 km was 2.5 hrs more than the time taken in the return journey.

\(\Rightarrow \frac{150}{a-10}-\frac{150}{a}=2.5\)

⇒ 150(a – a + 10) = 2.5a(a – 10) 

⇒ 1500 = 2.5a² – 25a 

⇒ a² – 10a – 600 = 0 

⇒ a² – 30a + 20a – 600 = 0 

⇒ a(a – 30) + 20(a – 30) = 0 

⇒ (a + 20)(a – 30) = 0 

⇒ a = 30 km/hr