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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Answers
Answer:
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.
Given: 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.
To find: Time taken of homeowner helps the roofer
Explanation: Days it will take the home owner to roof the house= 12 days
Homeowner's one day work= 1/12 of the work
Days it will take the professional roofer to roof the house= 4 days
Professional roofer's one day work= 1/4 of the work
If the homeowner helps the roofer, one day's work will be the sum of their individual daily work.
Work done in one day = 1/12 + 1/4
= 1+3 / 12
= 4/12
= 1/3
Therefore, 1/3 of the work is completed in one day if both work together.
Therefore, total days taken if both work together=
= 1/ (1/3)
= 3 days
Therefore, it will take 3 days to roof the house if the homeowner helps the roofer.