Question

The time taken by a person to cover 150kms was 2.5 hrs more than the time taken in the return j ourney. If he returned at a speed of 10km/ 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 x (S+10) - 150 x S= S x (S+10) x 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 = 20km/ hr and while return, its 30km/ hr