__Category__: Algebra, Mechanics, Physics"Published in Newark, California, USA"

The local train is 25 miles down the track from Central Station when the express leaves the station. The local train travels at a rate of 50 mi/hr and the express travels travels at a rate of 80 mi/hr. Let n represent the number of hours since the express train left Central Station.

(a) Write an expression that represents the express train's distance from Central Station in n hours.

(b) When will the express train catch up with the local train?

__Solution__:

To illustrate the problem, it is better to draw the figure as follows

Photo by Math Principles in Everyday Life |

Initially, the local train is already left from Central Station which is 25 miles apart. The time traveled by the local train is

If the express train leaves from Central Station which is faster than the local train, then the express train will catch up the local train at time n.

Photo by Math Principles in Everyday Life |

(a) The distance traveled by the express train is

(b) Finally, the express train will catch up the local train at

or