Question

The distance between Ahmedabad and Vadodara is 100 km. Two trains set-off simultaneously from Ahmedabad and Vadodara towards each other. The speeds of these trains are \[45\text{ }km/h\] and \[30\text{ }km/h\] respectively. When will they cross each other?

Answer 1

Hint: Since the value of speed of the train has been given and distance would be found out, therefore use the formula of speed which is distance per unit time. Since the time taken by both trains are the same. So equate both formulas of speed. Then calculate the value of distance where these two trains will cross each other.

Complete step-by-step answer:

Let, $ A $ be the train released from Ahmedabad having speed \[45\text{ }km/h\] and $ B $ be the train released from Vadodara having speed \[30\text{ }km/h\] .
Let, O be the point where the train will cross.
Let $ x $ be the distance from A to point O then $ 100-x $ will be the distance from B to O. Since the total distance between $ A\text{ and }B $ is \[100km\] .
If t be the time taken by both the train to reach at point O then
 $ \text{speed}\left( \text{A} \right)=\dfrac{\text{distance}}{\text{time}\left( t \right)}\text{ }\!\!\And \!\!\text{ speed}\left( \text{B} \right)\text{=}\dfrac{\text{distance}}{\text{time}\left( t \right)} $
Put the values in both formulas. We get,
 $ \begin{align}
  & 45km/h=\dfrac{x}{t}\text{ }\!\!\And\!\!\text{ 30km/h=}\dfrac{100-x}{t} \\
 & t=\dfrac{x}{45}\text{ }\!\!\And\!\!\text{ t=}\dfrac{100-x}{30} \\
\end{align} $
Now equate both equations. We get,
 $ \begin{align}
  & \dfrac{x}{45}=\dfrac{100-x}{30} \\
 & 30x=4500-45x \\
 & 75x=4500 \\
 & x=60km \\
\end{align} $
So these two trains will cross each other a distance of 60km from $ A $ and $ 100-x=100-60=40km $ from $ B $.

Note: In this question, we have taken time for both the trains to cross each other is the same. Even though speed is different, time taken by trains will be different. Students may get confused like, velocity is different therefore time must be different but this is not always true. If speed of first body is greater than next then might be distance covered by first body will be more but time taken to reach at a point were both body will cross must be same.