SOLUTION: A painter works on a job for 10 days and is then joined by her helper. Together they finish the job in 6 more days. Her helper could have done the job alone in 30 days. How long wo

Question 127714: A painter works on a job for 10 days and is then joined by her helper. Together they finish the job in 6 more days. Her helper could have done the job alone in 30 days. How long would it have taken the painter to do the job alone?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A painter works on a job for 10 days and is then joined by her helper. Together they finish the job in 6 more days. Her helper could have done the job alone in 30 days. How long would it have taken the painter to do the job alone?
:
Let x = time required by the painter to do the job alone
:
Let the completed job = 1
:
Think of of it this way. The painter has 10/x of the job completed when he's joined by the helper
+ + = 1
same as:
+ = 1
:
Multiply equation by 30x to get rid of the denominator
30x* + 30x* = 30x(1)
:
30(16) + 6x = 30x
480 + 6x = 30x
480 = 30x - 6x
480x = 24x
x =
x = 20 days, painter by himself
:
:
We can check that using the original equation
+ + =
+ + = 1
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