SOLUTION: Juan can paint the neighbor's house four times as fast as Ariel. The year they worked together it took them 8 days. How long would it take each to paint the house alone?

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Question 297556: Juan can paint the neighbor's house four times as fast as Ariel. The year they worked together it took them 8 days. How long would it take each to paint the house alone?
Found 2 solutions by richwmiller, MathTherapy:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
8/4a+8/a=1
2/a+8/a=1
2+8=a
10=a
j=10/4=2.5

Answer by MathTherapy(10559) About Me  (Show Source):
You can put this solution on YOUR website!
Juan can paint the neighbor's house four times as fast as Ariel. The year they worked together it took them 8 days. How long would it take each to paint the house alone?

Let the amount of days Juan takes to do the job be J

Since Juan works 4 times faster than Ariel, then Ariel's time to do the entire job is 4J

This means that Juan can do 1%2FJ of the job in 1 day, and

Ariel can do 1%2F4J of the job in 1 day

Now we get: 8%2F%28J%29+%2B+8%2F%284J%29+=+1 since it takes both men 8 days to do the entire job

This gives us: 32 + 8 = 4J --------- Mutiplying by LCD, 4J

40 = 4J

Therefore, J, or Juan's time to do the job is: 40%2F4 or highlight_green%2810%29 days, which means that Ariel can do the same job in 10*4 days, or highlight_green%2840%29 days.