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/h more than the speed when going, find his speed per hour in each direction. 

Answer 1

Let the speed of the person be S, Hence return speed of the person = S + 10.

D = 150 Km, Time = Distance/Speed. Time difference = 2.5 Hours 

Hence, in these two conditions, 

`150/"S" - 150/("S"  + 10) = 2.5`

⇒ 150 × (S + 10) − 150 × S = S × (S + 10) × 2.5 

⇒ 2.5 s² + 25 s − 1500 = 0 

⇒ 25 s² + 250 s − 15000 = 0

⇒  S² + 10 S − 600 = 0 

⇒ S² + 30S − 20S − 600 = 0 

⇒ S (S + 30) − 20 (S + 30) = 0

⇒ (S + 30) (S − 20) = 0

As the speed can’t be negative, S = 20 km/hr and while return, its 30 km/hr