Two trains, each of length 90 metres, run on parallel...

Two trains, each of length 90 metres, run on parallel tracks. When running in the same direction, the faster train passes the slower train completely in 18 seconds, but when they are running in opposite directions approaching each other at the same speeds as before they cross each other in 9 seconds. Find the speed of each train. (a) $9 \mathrm{~m} / \mathrm{sec}$., $15 \mathrm{~m} / \mathrm{sec}$. (b) $7 \mathrm{~m} / \mathrm{sec} ., 5 \mathrm{~m} / \mathrm{sec}$. (c) $15 \mathrm{~m} / \mathrm{sec}$., $5 \mathrm{~m} / \mathrm{sec}$. (d) None of these

Two trains, each of length 90 metres, run on parallel tracks. When running in the same direction, the faster train passes the slower train completely in 18 seconds, but when they are running in opposite directions approaching each other at the same speeds as before they cross each other in 9 seconds. Find the speed of each train.
(a) $9 \mathrm{~m} / \mathrm{sec}$., $15 \mathrm{~m} / \mathrm{sec}$.
(b) $7 \mathrm{~m} / \mathrm{sec} ., 5 \mathrm{~m} / \mathrm{sec}$.
(c) $15 \mathrm{~m} / \mathrm{sec}$., $5 \mathrm{~m} / \mathrm{sec}$.
(d) None of these

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Key Concepts

Relative Speed

Relative speed is the speed of one object as observed from another moving object. In problems involving two moving objects, when they travel in the same direction, the relative speed is the difference between their speeds, and when they travel in opposite directions, the relative speed is the sum of their speeds. This concept is fundamental in determining the rate at which the distance between the objects changes.

Time-Distance Relationship

The time-distance relationship is built upon the formula: distance = speed × time. This principle allows one to calculate any one of these three variables if the other two are known. When two objects pass each other, the combined length or distance covered is critical for setting up the equations necessary for solving the problem.

Solving Simultaneous Equations

When multiple conditions are provided, such as different relative speeds in different scenarios, simultaneous equations are set up based on these conditions. Solving these equations simultaneously is crucial for finding the unknown values, like the speeds of the moving objects. This method utilizes the relationships derived from the time-distance equation and relative speed concept.

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