1950 AHSME Problems/Problem 29
Problem
A manufacturer built a machine which will address envelopes in minutes. He wishes to build another machine so that when both are operating together they will address envelopes in minutes. The equation used to find how many minutes it would require the second machine to address envelopes alone is:
Solution
Solution 1
We first represent the first machine's speed in per minutes: . Now, we know that the speed per minutes of the second machine is Now we can set up a proportion to find out how many minutes it takes for the second machine to address papers:
. Solving for , we get minutes. Now that we know the speed of the second machine, we can just plug it in each option to see if it equates. We see that works.
Solution 2
First, notice that the number of envelopes addressed does not matter, because it stays constant throughout the problem. Next, notice that we are talking about combining two speeds, so we use the formula , where are the respective times independently, and is the combined time. Plugging in for and , we get .
Taking a reciprocal, we finally get .
See Also
1950 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 28 |
Followed by Problem 30 | |
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