1973 AHSME Problems/Problem 14
Problem
Each valve , , and , when open, releases water into a tank at its own constant rate. With all three valves open, the tank fills in 1 hour, with only valves and open it takes 1.5 hours, and with only valves and open it takes 2 hours. The number of hours required with only valves and open is
Solution
Let the rate of water flowing through valve be , the rate of water flowing through valve be , and the rate of water flowing through valve be . WLOG, let the volume of the tank be 1 liter, and let the units for the rates be liters per hour. With this information, we can write three equations. Manipulate each equation to get Solving for yields , and solving for yields . The number of hours to fill the tub with only valves and on is .
See Also
1973 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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