Math CentralQuandaries & Queries


Question from beket, a student:

you and your friend leave your home town at the same time your friend travels by train 45 mph directly east while you travel by train 50 mph going directly south you are talking on cell phone but you plan charges extra if the phones are 100 miles apart. How long will you and your friend be able to talk before the charges increase?

Hi Beket,

Draw a diagram!


T is the train station, F is your friend and Y is you. From the diagram it is clear that |FY|, the distance between your friend and you is the hypotenuse of a right triangle. Hence this is a problem for Pythagoras' Theorem.

After you have travelled for t hours how far have you travelled? This is |TY|. How far has your friend travelled? What is the distance |FY|? This is 100 miles. Solve for t.


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