Question

2 trains starting at the same time from 2 stations 200 km apart and going in opposite direction cross each other at a distance of 110 km from one of the stations . what is the ratio of their speeds ?

Answer 1

$11:9$

Explanation:

The question is asking about the ratio of their speeds and not the ratio of their distances, so let us see what we can do with the given information.

Remember that 

\[\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}\]

Since the time it took for both trains to reach the meeting point is the same, we will treat time like a constant. So the two variable that we have are Speed and Distance.

These two variables can now be represented by the relationship

\[\text{Speed} \quad \alpha \quad \text{Distance}\]

Using this relationship we can use Distance as a proxy for speed in our calculations

So, Train A has covered $110$km whilst Train B has covered $90$km

\[\text{Speed of A}: \text{Speed of B} = 110 : 90 \]

Simplifying gives

\[\text{Speed of A}: \text{Speed of B} = 11 : 9 \]