Question

While Sonia takes a walk, Rahul rides his bicycle along with her in the same direction. As soon as they
got out of the gate, Rahul rides towards the end of the road and rides back to Sonia. He repeats this
one more time (2 rounds in total). riding at a uniform speed. After the second time, both of them walk
last 45 meters together, the total distance between their house gate and the end of the road is 125
meters. Sonia walks at the rate of 4 m/sec. What is the cycling speed of Rahul?​

Answer 1

Rahul cycling speed is 17m/s.

Given:

While Sonia takes a walk, Rahul rides his bicycle along with her in the same direction.

As soon as they got out of the gate, Rahul rides towards the end of the road and rides back to Sonia.

He repeats this one more time (2 rounds in total). riding at a uniform speed. After the second time, both of them walk last 45 meters together, the total distance between their house gate and the end of the road is 125 meters. Sonia walks at the rate of 4 m/sec.

To find:

Cycling speed of Rahul

Solution:

Rahul rides towards the end of road and back to Sonia two times.

In the same time, Sonia covers 'x' distance.

The distance between Gate and end of road is 125m.

After cycling two times the distance between Sonia and end of road is 45metres.

It is given that Sonia walks at a speed of 4m/s. The distance covered by Sonia while Rahul cycled twice towards the end of road and Sonia is is 80metres.

The distance covered by Rahul before they together started walking is 125 + 2*(125- 1st time back to Sonia) + (125- 2nd time back to Sonia)

The distance covered by Sonia when Rahul 1st came back to her is

⇒ 80 meters/2 = 40m

So, the distance covered by Rahul before they together started walking is,

⇒ 125 + 2*(125-40)+(125-80)

⇒ 125+ 2*(85)+(45)

≅ 125+170+45 = 340m

The distance that they walked together is 45m

We know that, Speed = distance/time

The cycling speed of Rahul is,

Rahul Speed = Distance covered by Rahul/ time taken

∵ Speed of Sonia is 4m/s. She covered a distance of 80m.

⇒ Time taken = 80/4 = 20s

Rahul speed = 340/20 = 17m/s.

Hence proved.

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