Question

A and B are two stations 390 km apart. A train starts from A at 10 a.m. and travels towards B at 65 kmph. Another train starts from B at 11 a.m. and travels towards A at 35 kmph. At what time do they meet?

Answer 1

Hint: First of all find the distance travelled by a train starts at station A from 10 a.m. to 11 a.m. which is 1 hour and it is given that train starting from station A travels 65 kmph meaning in hour it covers 65 km distance so from 10 a.m. to 11 a.m. it covers the distance 65 km. Then find the remaining distance that needs to travel so that A and B meet at some point which is calculated by subtracting 65 km from 390 km. Hence, we got the relative distance from 11 a.m. till the point the two trains meet. Now, find the relative speed of the two trains as the two trains are approaching each other so relative speed is calculated by adding the speeds of the two trains. Now, we know the relative distance, relative speed, we can find the relative time by using the following formula $\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}$. The time when the two trains meet is the addition of 11 a.m. to the relative time.

Complete step by step answer:
It is given that two trains are 390 km apart. And a train starts from station A at 10 a.m. while the other train starts from station B at 11 a.m. Both the trains starting from A and B have different speeds which are given as 65 kmph and 35 kmph.
Let us assume that the train which leaves from station A is train A and the train which leaves from station B is train B.
Now, we are going to find the distance travelled by train A from 10 a.m. to 11 a.m. The time interval between these times is 1 hour and we know that speed of the train A is 65 kmph meaning it covers a distance of 65 km in 1 hour meaning in 1 hour (i.e. from 10 a.m. to 11 a.m.) the distance travelled by train A is 65 km. Then the remaining distance is equal to:
$\begin{align}
  & 390-65 \\
 & 325km \\
\end{align}$
Now, we are applying the relative concept between the two trains. The relative speed of the two trains are calculated by adding the speeds of both the trains because the two trains are approaching each other.
Relative speed of the two trains is equal to:
$\begin{align}
  & 65+35 \\
 & =100kmph \\
\end{align}$
And the distance traversed by the two trains is equal to 325 km because before 11 a.m. train B had not started so we cannot include the total distance.
The time at which both the trains will meet is calculated by the following formula:
$\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}$
Substituting speed as 100 kmph and distance as 325 km in the above equation we get,
$\begin{align}
  & 100=\dfrac{325}{\text{Time}} \\
 & \Rightarrow Time=\dfrac{325}{100}=3.25hours \\
\end{align}$
The time when the two trains meet is calculated as follows:
$\begin{align}
  & 11a.m.+3.25hours \\
 & =2:25p.m. \\
\end{align}$

Hence, the time when the two trains A and B meet is equal to 2:25 p.m.

Note: You might be thinking, how we get the addition of 11 a.m. to 3.25 hours as 2:25 p.m. which we are going to show below:
3.25 hours meaning 3 hours and 25 minutes. So, we have added 3 hours at 11 a.m. When we add 3 hours in 11 a.m. then the clock will show 2 p.m. After that we have added 25 minutes to 2 p.m. If we add 2 p.m. to 25 minutes, then the clock will show 2:25 p.m.