Question

The distance between two stations is 340 km. Two trains start simultaneously from these stations on parallel tracks and cross each other. The speed of one of them is greater than that of the other by 5 km/hr. If the distance between two trains after 2 hours of their start is 30 km., find the speed of each train.

Answer 1

Hint: First we let the speed of the first train be ‘r’ in one hour and the other train speed greater than 5 with respect to the first train. This implies that the speed of the second train be ‘r + 5’ in one hour. Now, we easily calculate the speed of both the trains in 2 hours. We subtract 30km from 340km and add both the distance of the train in 2 hours and put it equal to 310km. By this we get both the distances.

Complete step-by-step answer:
Let the ‘r’ be the speed of the first train.
Similarly, the speed of the second train is ‘r + 5‘.
The distance travelled by first train in 2 hours\[=2r\].
The distance travelled by second train in 2 hours\[=\left( r+5 \right)\times 2=2\left( r+5 \right)\].
Now, we know that the distance the first train travels i.e. ‘2r’ plus the distance the other train travels i.e. ‘2(r+5)’ is equal to \[340-30=310\].
This implies that
\[\begin{align}
  & \begin{array}{*{35}{l}}
   2r+2\left( r+5 \right)=310 \\
   \Rightarrow 2r+2r+10=310 \\
   \Rightarrow 4r=300 \\
\end{array} \\
 & \Rightarrow r=75 \\
\end{align}\]
Thus, the speed of the first train is 75 kmph.
Speed of other train:
$\begin{align}
  & \Rightarrow r+5 \\
 & \Rightarrow 75+5 \\
 & \Rightarrow 80 \\
\end{align}$
Therefore, the speed of other trains is 80 kmph.
This implies that the speed of the first train is 75 kmph and the second train is 80 kmph.

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 speed of trains. In this way, we can calculate the respective speed of each train.