A bicyclist travels downhill at 12 mph, on the level at 8 mph, and uphill at only 6 mph. The bicyclist takes 4 hours to travel from town A to town B. The return trip takes 4 hours and 30 minutes. Find the distance between the two towns.
Solution by Mallory Sparr , Alamo Heights High School, San Antonio, TX
Approaching this problem I immediately began to solve it as a system of equations. The first equation would represent the time it took for the first half of the trip, and the second equation would be the time for the return trip. Let d = miles traveled downhill, l = miles traveled on a level surface, and u = miles traveled uphill. Therefore, our two equations would be:
Adding these two equations gives us:
Multiplying both sides by 4, we get:
miles.
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