SOLUTION: Three friends anil, bala and chetan, from X to town X to town Y which was 4o km. Anil who had a bike started along with bala while chetan started simultaneously on foot. After some

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Question 1055579: Three friends anil, bala and chetan, from X to town X to town Y which was 4o km. Anil who had a bike started along with bala while chetan started simultaneously on foot. After some time , anil dropped bala on the way and went back to pick up chetan while bala proceeded to Y on foot. Anil picked up chetan and reached Y at the same time as bala. Anil traveled at 50km/hr. The speed at which bala and chetan walked was 10 km /hr . find the time after which anil turned back ?
Answer by ikleyn(52810)   (Show Source): You can put this solution on YOUR website!
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Three friends Anil, Bala and Chetan, traveled from town X to town Y which was 40 km.
Anil who had a bike started along with Bala while Chetan started simultaneously on foot.
After some time, Anil dropped Bala on the way and went back to pick up Chetan while Bala proceeded to Y on foot.
Anil picked up Chetan and reached Y at the same time as Bala. Anil traveled at 50km/hr.
The speed at which Bala and Chetan walked was 10 km/hr. Find the time after which Anil turned back?

Below is the sketch to solve the problem:

                       d     d
     X--------------p-----c-----q--------------Y


You see the points X and Y here. The distance between X and Y is 40 kilometers.
The point q is the point where Anil dropped Bala on the way and went back to pick up Chetan.
The point p is the point where Anil picked up Chetan.

So, the Anil's   way is  Xq, then qp,  then pY.
    the Bala's   way is  Xq  biking    with Anil, then qY walking.
    the Chetan's way is  Xp  walking,  then  pY   biking with Anil.

The point "c" is the central point at the half of the distance between X and Y.

From the symmetry, it is clear that the distance Xp is equal to qY.
     The ratio for it is the fact from the condition that all three travelers came to Y simultaneously.
It means that pc = qc, and all we need to do is to find the length pc or qc.
I marked this distance as "d" in the sketch:  d = pc = qc.

Anil on his bike covered the distance of  Xq + 2d + 2d + qY = 40 + 4d.
He spent  hours for the entire journey.

Bala   spent  hours.

Chetan spent  hours, the same time as Bala.

So, the equation to find the unknown "d" is

 = .

Actually, the problem is just setup and, therefore, solved.
The rest is just arithmetic.

The answer is d = 10 km.

So, Xq =  = 30 kilometers, and Anil covered Xq in  =  of an hour = 3*12 = 36 minutes.
It is the time after which Anil turned back.

The problem is solved.

This problem is classic Travel and Distance problem.
I remember it from my childhood time,  but I never solved it before.
It is the first time I solved it.

Thanks to the person who posted it,  for beautiful challenge.

By the way, this complicated logistic provides the minimal time for three travelers, who have only one bike, to reach the final point.


In response,  you can see the bunch of Travel and Distance problems in this site under the link  Travel and Distance problems

They are the part of my online textbook
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

You are welcome!


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