1954 AHSME Problems/Problem 30
Problem
and together can do a job in days; and can do it in four days; and and in days. The number of days required for A to do the job alone is:
Solution
Let do of the job per day, do of the job per day, and do of the job per day. These three quantities have unit . Therefore our three conditions give us the three equations: We divide the three equations by the required constant so that the coefficients of the variables become 1: If we add these three new equations together and divide the result by two, we obtain an equation with left-hand side , so if we subtract (the value of which we know) from both equations, we obtain the value of , which is what we wish to determine anyways. So we add these three equations and divide by two: Hence: This shows that does one third of the job per day. Therefore, if were to do the entire job himself, he would require days.
See Also
1954 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 29 |
Followed by Problem 31 | |
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