# Can you solve this without making any equation??

In the above image a boy is at a point in the tunnel AB, dividing it in the ratio 2:3. A train is approaching the side A with a constant speed. Now at a particular instant of time, the situation is such that if the boy runs towards A the train enters the tunnel just as he come out. And if he decides to go towards B, then the train and the boy both will come out at the same time. Our job is to find the ratio between their speeds. The real task is doing this by the most elementary method that is possible.

Note by Sanjeet Raria
7 years, 1 month ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$

Sort by:

5:1

- 7 years, 1 month ago

Your answer is correct but here I'm more concerned towards the method of solving it.

- 7 years, 1 month ago

Suppose speed is same....1:1..and take the length of the tunnel as 5m...so dist btwn man to A is 2m and man to B is 3m....now if ratio is 1:1 then if man runs towards A he will cover 2m and train will also cover 2m bcoz speed is same....so train is 2m away from the tunnel....now in 2nd case man runs towards B so he will cover 3m and train will also cover 3m..but in this case train will be at 1m away from pnt A in the direction of B...so our assumption 1:1 is incorrect....let the ratio 2:1...then in 1st case we came to know that train is 4m away from pnt A...and when man will be at B train will be 2m away from pnt A towards B....so 2:1 is also wrong....by this way we can find that 5:1 satisfies both cases...and it is the right ans...soln is quite lengthy but it is easy...

- 7 years, 1 month ago

This is very long in its sense man!

- 7 years, 1 month ago

Well, when the boy covers 2 m , the train reaches A. Now let the boy run towards B. When he'd cover 2m of distance the train would just reach A. Now pause here and take a look, the boy has 1m to go next and while he will cover this unit distance, the train will be covering 5m and they will come out together. That means in the same amount of time the boy covers 1m and train covers 5m. It means ratio of their velocity is 1:5

- 7 years, 1 month ago

Well, when the boy covers 2 m , the train reaches A. Now let the boy run towards B. When he'd cover 2m of distance the train would just reach A. Now pause here and take a look, the boy has 1m to go next and while he will cover this unit distance, the train will be covering 5m and they will come out together. That means in the same amount of time the boy covers 1m and train covers 5m. It means ratio of their velocity is 1:5

- 7 years, 1 month ago

Ohh....this is really a very nice way of thinking...nice solution

- 7 years, 1 month ago