Question

Aaron and Rachel can clear the weeds out of their vegetable garden in 2 hours if they work together. If Aaron works alone, it will take him 5 hours. How long long it take Rachel if she works alone?
a. 3 hours
b. 7 hours
c. 10/3 hours
d. none of these​

Answer 1

Answer:

c. 10/3 hours

Step-by-step explanation:

Let's make a table.  

Names:| Times completed in:|  Field Space Covered:| Rate the field was                                                                                                                                                                  .                                                                                                  covered:

Aaron   |       5 hours               |           1  field                 |  1/5 field space/hour

Rachel  |      x   hours              |           1   field                |   1/x field space/hour

Together|       2 hours             |           1   field               |    1/2 field space/hour

The 1 field represents that they covered the whole field.

The rate is found by dividing field space covered by amount of hours it took for them to cover it.

There rates individually should add up to the "together" rate.

$\frac{1}{5}+\frac{1}{x}=\frac{1}{2}$

Clear fractions by multiplying both sides by $5 \cdot 2 \cdot x=10x$ on both sides:

$10x \cdot \frac{1}{5}+10x \cdot \frac{1}{x}=10x \cdot \frac{1}{2}$

$2x+10=5x$

Subtract 2x on both sides:

$10=3x$

Divide both sides by 3:

$\frac{10}{3}=$

x represented the amount of time it took Rachel alone to cover 1 field.

10/3 hours is the answer.