1950 AHSME Problems/Problem 29
Contents
[hide]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 $\boxed{\textbf{(B) \frac{1}{8}+\frac{1}{x}=\frac{1}{2}}}$ (Error compiling LaTeX. Unknown error_msg) 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 $\boxed{\textbf{(B) \frac{1}{8}+\frac{1}{x}=\frac{1}{2}}}$ (Error compiling LaTeX. Unknown error_msg)
==See Also==
1950 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 28 |
Followed by Problem 30 | |
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