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

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) (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
----
Then 105/(12/7) = 61.25 days
===========================================

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?
---
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)
============
Cheers,
Stan H.
================

RELATED QUESTIONS
In Rural Housing Plan, 42% of the houses have second floor and garage, 60% have second... (answered by stanbon)

You are in the market for a new home. You're looking at a housing community. As you leave (answered by rfer)

Again I beleive I have a, b done but need help with c, can someone help please? 2. As... (answered by stanbon)

Betty and karen have been hired to paint the houses in a new development. Working... (answered by nerdybill)

Betty and Karen have been hired to paint the houses in a new development . Working... (answered by josgarithmetic)

Eric and Ryan have been hired to paint the houses in a new development. Working together... (answered by ewatrrr,Alan3354,TimothyLamb)

Please help me solve this equation: Pack-Em-In Real Estate is building a new housing... (answered by josmiceli)

a) The sales representative here tells you they also have two floor plans available, but... (answered by stanbon)

Could you please help me solve this problem I am not very good with word problem. As... (answered by vleith)