How To Solve a Math Word Problem About Trains


Word problems involving trains usually go something like this:

A train track is 300 miles long. On one end of the track, Train A leaves the station at 4 p.m. On the opposite end of the track, Train B leaves leaves at 6 p.m.. If Train A travels 45 mph and Train B travels 60 mph, when will they meet?

These math problems involve time, distance and speed, and can be difficult to solve because there are many variables to work with.

  • Draw a diagram of the track on a sheet of paper and in the top corner write three formulas that relate distance, speed and time:

    D = ST
    S = D/T
    T = D/S

    Whenever you know two quantities, you always can find the third with one of these math formulas.

  • Remember the following principle about objects moving in opposite directions: The speed at which the distance between the objects decreases is equal to the sum of the speeds of the objects.

    Using the example given in the intro, if Train A and Train B are moving toward each other at 45 mph and 60 mph respectively, then the distance between A and B is shrinking at a rate of 105 mph.

  • Adjust the problem so that both trains start at the same time.

    In the example, Train A starts two hours earlier. In those two hours, Train A travels two hours at 45 mph, which equals 90 miles. So at 6 p.m., when Train B starts, the trains are 210 miles apart: 300 miles as beginning distance minus 90 miles already covered by Train A equals 210 miles.

  • Use the principle in Step 2 to calculate when the trains will meet.

    At 6 p.m. the trains are 210 miles apart and moving toward each other at a combined rate of 105 mph. The time it take for the distance to shrink from 210 to 0 is calculated:

    T = 210 miles/105 mph
    = 2 hours.

    If the trains will meet in two hours from the starting time of the second train, which is 6 p.m., then they will meet at 8 p.m.

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