Question 415789
A new housing development will have 105 houses. All the houses have the same floor plan and dimensions. Carlos can paint a house by himself in 4 days. Manuel can paint a house in 3 days. 
a. A normal work week is 5 days. How many weeks will it take them working together to paint all 105 houses?
Find the "together rate".
1/4 + 1/3 = 1/x
3x + 4x = 12
x = 12/7 days
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Then 105/(12/7) = 61.25 days
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b. Suppose they need to finish in 28 weeks but can add only one worker. What is the greatest number of days the third worker can take to paint each house?
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1/4 + 1/3 + 1/x = 1/28
Multiply thru by 84x to get:
21x + 28x + 28 = x
48x = 28
x = 7/12 day (3rd worker time to paint a house)
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Cheers,
Stan H.
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