Some please help Harry can rake the leaves in the yard 8 hours faster than his little brother Jimmy can. If they work together,
they can complete the job in 3 hours. Using complete sentences, explain each step in figuring out how to determine the time it would take Jimmy to complete the job on his own.
use rates, the rate a person is working is the reciprocal of the time
working together, they work at a rate of 1/3 job per hour
when two people work together their rates add together
---> 1/h + 1/j = 1/3
---> h = j - 8 (harry takes 8 hrs less than jimmy)
substitute and solve for j
<span><span>1<span>j−8</span></span>+<span>1j</span>=<span>13</span></span>
combine fractions
<span><span><span>j+(j−8)</span><span>j(j−8)</span></span>=<span>13</span></span>
cross-multiply
<span><span>j2</span>−8j=6j−24</span>
<span><span>j2</span>−14j+24=0</span>
Factor
<span>(j−12)(j−2)=0</span>
j = 12
It takes jimmy 12 hours to rake the leaves
The answer is 10 whole loaves. We get this answer by dividing 8 by (3/4). Which results in decimal points as 10.6. Therefore meaning only 10 loaves were whole.
