Question

A and B are 2 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: In this problem first, we evaluate the distance travelled by train A after starting from 10 a.m. up to 11:00 a.m. at a speed of 65 kilometer per hour. At 11:00 a.m. train B also starts moving from another station with the speed 35 kilometer per hour. The distance obtained when a train travelled up to 11 is subtracted from 390 kilometer. Now the net distance between two trains is evaluated and is equated with time.

Complete step-by-step answer:
As per the data given in the problem statement,
The distance between two stations = 390 km
Speed of train A after starting at 10 a.m. = 65 kmph
Speed of train B after starting at 11 a.m. = 35 kmph
Let, the distance travelled by train A in one hour be D.
Also, by using the speed formula: $speed=\dfrac{dis\tan ce}{time}$.
This implies that the total distance covered by 11 a.m. is
 $\begin{align}
  & D=speed\times time \\
 & =65\times 1 \\
 & =65km \\
\end{align}$

After 11 a.m. the train B also starts moving. This implies that the net distance left between the trains = 390 – 65 = 325 km.

Let, t be the time after which both the trains meet.
This implies that distance covered by train A in time t $=speed\times time=65t$ .
Also, distance covered by train B in time t $==speed\times time=35t$.
The sum of the distance must be equal to 325 km.
$\begin{align}
  & 65t+35t=325 \\
 & 100t=325 \\
 & t=\dfrac{325}{100} \\
 & t=3.25hours \\
\end{align}$
 This implies that they will meet after 11 + 3.25 = 14.25 i.e. 2:25 p.m.
Note: The key step in solving this problem is the knowledge of the relationship between speed and distance. By using the statement provided in the question we can easily formulate expressions for distance of trains. Students must take care that they are adding time in the final expression. Also, time must be represented in p.m. because the given data is in a.m.