Question

37.
The time taken by a person to cover 150 km was 2.5 hrs more than the time taken in the return journey. If he
returned at a speed of 10 km/hr more than the speed of going, what was the speed per hour in each direction?
(a) 15 km/hr, 30 km/hr.
(b) 25 km/hr, 30 km/hr.
(c) 20 km/hr, 15 km/hr.
(d) 20 km/hr, 30 km/hr.

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Answer 1

Answer:

Here is the solution:

Step-by-step explanation:

let the time be 't' hours for returning the journey

*according to the question*

for the man for journey, the time taken is t+2.5hrs

speed=150/t=2.5

while returning,

speed=150/t that is 10km/h more than 150/t+2.5

therefore; 150/t-150/t+2.5=10

150t+375-150t=10t^2+2.5t

10^2+2.5-375=0

t=5

speed=20km/h

return speed=30km/h

Answer 2

Step-by-step explanation:

⇒ 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