SOLUTION: 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

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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?
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?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
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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