Sum

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.

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#### Solution

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`1/2` h

`:.(150`

`=>150/x-150/(x+10)=5/2`

`=>(150x+1500−150x)/(x(x+10))=5/2`

⇒x^{2}+10x=1500×`2/5`=600

⇒x^{2}+10x−600=0

⇒x^{2}+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

Concept: Quadratic Equations

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