Question

The time taken by a person to cover 150 km was 2 1/2 hours more than the time taken in the return journey. If he returned at a speed of 10 km/hour more than the speed while going, find the speed per hour in each direction.

Answer 1

Let the speed of the person while going be x km/h.

⇒ Speed of the person while returning = (x + 10) km/h

Time taken by the person while going = Time taken by the person while returning + 2${\displaystyle \frac{1}{2}}$ h

${\displaystyle \therefore (150}$

${\displaystyle \Rightarrow \frac{150}{x}-\frac{150}{x+10}=\frac{5}{2}}$

${\displaystyle \Rightarrow \frac{150x+1500-150x}{x(x+10)}=\frac{5}{2}}$

⇒x²+10x=1500×${\displaystyle \frac{2}{5}}$=600

⇒x²+10x−600=0

⇒x²+30x−20x−600=0

⇒x(x+30)−20(x+30)=0

⇒(x+30)(x−20)=0

⇒x−20=0 or x+30=0

⇒x=20, −30

Since speed cannot be negative, x = 20.

⇒ Thus, speed of the person while going = 20 km/h

⇒ Speed of the person while returning = 20 + 10 = 30 km/h