Math CentralQuandaries & Queries


Question from J, a parent:

Two trains left the city at the same time, traveling in opposite directions. The eastbound train travels for ten hours and the westbound train travels for 5 hours. They are now 1300 km apart. The westbound train's rate is 20 km/hr faster than the eastbound train. Find the speed of each train.

any help you can provide would be much appreciated.


Hi J,

The key here is that distance = time × rate. What you are missing is the rate of the eastbound train for if you can determine it then the rate of the westbound train is 20 km/hr faster. So let r be the rate of the eastbound train in km/hr and then the rate of the westbound train is (r + 20) km/hr.

distance = time × rate so for the eastbound train distance = 10 × r miles.

What is the distance the westbound train travels? The sum of these distances is 1300 km. Solve for r.


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