The time taken by a person to cover the 150 km per hour was 2 and half hours more than the time taken in the return journey. If he return at a speed of 10 kn per hour more than the speed while going, find the speed per hour in each direction.
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Distance given =150km
⇒ Let the forward speed be x and the return speed will be x+10
We know that, Time=
speed
Distance
∴
x
150
=
x+10
150
+2.5
⇒ 150(x+10)−150x=2.5×x(x+10)
⇒ 150x+1500−150x=2.5x
2
+25x
⇒ 2.5x
2
+25x−1500=0
⇒ 25x
2
+250x−15000=0
⇒ x
2
+10x−600=0
⇒ x
2
+30x−20x−600=0
⇒ x(x+30)−20(x+30)=0
⇒ (x+30)(x−20)=0
The value of cannot be negative.
∴ Forward speed will be 20km/hr
⇒ Return speed =20+10=30km/hr
⇒ The required product =20×30=600km/hr
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