Question

Two trains run simultaneously, one of which is traveling from place C to B and the other is traveling from place B to C. After meeting, the two trains arrive at their destinations in 4 hours and 9 hours respectively. Find the ratio of their speeds.

• A. 4:3
• B. 4:5
• C. 3:2
• D. 3:4
• E. 2:3

Hint:

Remember that speed and time are inversely proportional. In the meeting-point formula, the time for the second train goes in the numerator to find the ratio of the first train's speed.

Answer 1

The Correct Option is C

To find the ratio of the speeds of the two trains, we will apply the concept of relative speeds and the fact that the time taken after the trains meet is inversely proportional to their speeds.

Let's assume the speed of the train traveling from place C to B is \(S_1\) and the speed of the train traveling from place B to C is \(S_2\).

When two trains moving towards each other meet, the distance each travels after meeting is inversely proportional to their speed. Hence, we have the relation:

The ratio of the speeds of the two trains will be the reverse of the ratio of time taken to reach the destinations after meeting.

\(\frac{S_1}{S_2} = \frac{T_2}{T_1}\)

Where \(T_1\) is the time taken by the train from C to B after meeting which is 4 hours, and \(T_2\) is the time taken by the train from B to C after meeting which is 9 hours.

Substituting the values, we get:

\(\frac{S_1}{S_2} = \frac{9}{4}\)

This shows the ratio of \(S_2\) to \(S_1\) is:

Reversing the ratio, we get:

\(\frac{S_2}{S_1} = \frac{4}{9}\)

Therefore, the correct option for the speed ratio of the train traveling from B to C to the train traveling from C to B is \(3:2\).

Hence, the correct answer is 3:2.