# 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 1 - Algebra

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.

#### 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 + 21/2 h

:.(150

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

=>(150x+1500−150x)/(x(x+10))=5/2

x2+10x=1500×2/5=600

x2+10x600=0

x2+30x20x600=0

x(x+30)20(x+30)=0

(x+30)(x20)=0

x20=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

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