1975 AHSME Problems/Problem 17
Problem
A man can commute either by train or by bus. If he goes to work on the train in the morning, he comes home on the bus in the afternoon; and if he comes home in the afternoon on the train, he took the bus in the morning. During a total of working days, the man took the bus to work in the morning times, came home by bus in the afternoon times, and commuted by train (either morning or afternoon) times. Find .
Solution
The man has three possible combinations of transportation: .
Let be the number of times the man takes the . Then, is the number of times he takes the . Keep in mind that and .
Let be the number of times the man takes the and . Now, we get the two equations and
Solving the system of equations, we get and .
So during the working days, the man took the on days, the on day, and the on days.
Therefore, . ~jiang147369
See Also
1975 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 16 |
Followed by Problem 18 | |
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