Question

A homeowner estimates that it will take him 12 days to roof his house. A professional roofer estimates that he could roof the house in 4 days. How long will it take if the homeowner helps the roofer? *
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please answer it quickly I need it right now

Answer 1

Step-by-step explanation:

First figure out how much of the job each could complete in one day

The homeowner would take 7 days so in one day he would complete 1/7 of the job

The roofer would take 2 days so in one day he would complete 1/2 of the job

Together they would complete 1/7 + 1/2 = 2/14 + 7/14 = 9/14 of the job in a day

Now we need to figure out how many days (D) it would take to complete the job (J)

if 9/14 of the job was done per day. Think of the whole job as a percentage.. we want J = 100%

which as a decimal is J=1

The logic is (9/14 day)(#days) = 100 % or (9/14)D = 1

(9/14)D = 1

D = 14/9

So together they would take 14/9 days or 1 5/9 days to complete the job

This makes sense because alone the roofer would take 2 days. With the homeowners help it should take less than 2 days.....