Question

A manufacturer built a machine which will address $500$ envelopes in $8$ minutes. He wishes to build another machine so that when both are operating together they will address $500$ envelopes in $2$ minutes. The equation used to find how many minutes $x$ it would require the second machine to address $500$ envelopes alone is:

$8-x=2$

$\dfrac18+\dfrac1x=\dfrac12$

$\dfrac{500}{8}+\dfrac{500}{x}=500$

$\dfrac{x}{2}+\dfrac{x}{8}=1$

None of these answers

Answer: B

Concepts:rate rational equation

Difficulty rating: 1440

Small Hint:

Measure each machine’s rate in batches of $500$ envelopes per minute

Big Hint:

The two individual rates must add to the combined rate

Solution:

The first machine completes $\tfrac18$ of a $500$ -envelope batch per minute, and the second completes $\tfrac1x$ of a batch per minute. Together they must complete $\tfrac12$ of a batch per minute. Therefore the required equation is $\frac18+\frac1x=\frac12.$

Thus, the correct answer is B.

1950 AMC 12 Problem 29

Answer: B

Difficulty rating: 1440

Small Hint:

Big Hint:

Solution:

Problem 29 in Other Years