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.
[tex]\frac{1}{5}+\frac{1}{x}=\frac{1}{2}[/tex]
Clear fractions by multiplying both sides by [tex]5 \cdot 2 \cdot x=10x[/tex] on both sides:
[tex]10x \cdot \frac{1}{5}+10x \cdot \frac{1}{x}=10x \cdot \frac{1}{2}[/tex]
[tex]2x+10=5x[/tex]
Subtract 2x on both sides:
[tex]10=3x[/tex]
Divide both sides by 3:
[tex]\frac{10}{3}=[/tex]
x represented the amount of time it took Rachel alone to cover 1 field.
10/3 hours is the answer.
