Question

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.

Answer 1

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

1j−8+1j=13 combine fractions j+(j−8)j(j−8)=13 cross-multiply j2−8j=6j−24 j2−14j+24=0 Factor (j−12)(j−2)=0 j = 12 It takes jimmy 12 hours to rake the leaves