SOLUTION: Kim can paint a barn in 5 days, and Alyssa can paint it in 8 days. Kim and Alyssa start painting a barn together, but after 2 days Alyssa gets sick and Kim finishes the work alone.
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-> SOLUTION: Kim can paint a barn in 5 days, and Alyssa can paint it in 8 days. Kim and Alyssa start painting a barn together, but after 2 days Alyssa gets sick and Kim finishes the work alone.
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Question 979866: Kim can paint a barn in 5 days, and Alyssa can paint it in 8 days. Kim and Alyssa start painting a barn together, but after 2 days Alyssa gets sick and Kim finishes the work alone. How long did it take Kim to finish painting the barn?
The explanation they gave in my book confused me, if anyone can break this down for me as simple as possible that would be great! Thank you :) Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Kim can paint a barn in 5 days, and Alyssa can paint it in 8 days.
Kim and Alyssa start painting a barn together, but after 2 days Alyssa gets sick and Kim finishes the work alone.
How long did it take Kim to finish painting the barn?
:
let t = no. of days it took Kim to finish after Al got sick
We know:
Al worked two days
and
Kim worked t+2 days
:
let the completed job = 1 (a painted barn)
:
A shared work equation, each will do a fraction of the job, the two fractions add up to 1 + = 1
multiply the equation by the least common multiple of 5 and 8
40* + 40* = 40(1)
Cancel the denominators and you have
8(t+2) + 5(2) = 40
8t + 16 + 10 = 40
8t + 26 = 40
8t = 40 - 26
8t = 14
t = 14/8
t = 1.75 days after Al quits
:
:
We can confirm this; Kim worked a total 3.75 days + =
.75 + .25 = 1
