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 this job on his own.

Question

Mathematics

Taylor Conley

27 September, 07:23

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 this job on his own.

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Blaze Page · 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-24j2-14j+24=0 Factor (j-12) (j-2) = 0 j = 12 It takes jimmy 12 hours to rake the leaves