SOLUTION: Mike, Joe and Bill are painting a fence. The painting can be finished if Mike and Joe work together for 4 hours and Bill works alone for 2 hours, or if Mike and Joe work together f

Question 499228: Mike, Joe and Bill are painting a fence. The painting can be finished if Mike and Joe work together for 4 hours and Bill works alone for 2 hours, or if Mike and Joe work together for 2 hours and Bill works alone for 5 hours, or if Mike works alone for 6 hours, Joe works alone for 2 hours and Bill works alone for 1 hour. How much time does it take each man working alone to complete the painting.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Mike, Joe and Bill are painting a fence.
The painting can be finished if Mike and Joe work together for 4 hours and Bill works alone for 2 hours, or if Mike and Joe work together for 2 hours and Bill works alone for 5 hours, or if Mike works alone for 6 hours, Joe works alone for 2 hours and Bill works alone for 1 hour.
How much time does it take each man working alone to complete the painting.
:
Write an equation for each scenario, let the completed job = 1
:
The painting can be finished if Mike and Joe work together for 4 hours and Bill works alone for 2 hours,"
+ + = 1
:
"if Mike and Joe work together for 2 hours and Bill works alone for 5 hours,"
+ + = 1
:
"if Mike works alone for 6 hours, Joe works alone for 2 hours and Bill works alone for 1 hour."
+ + = 1
:
We are going to use elimination here multiply the 2nd eq by 2, subtract the 1st equation
+ + = 2
+ + = 1
---------------------------------------subtraction eliminates m and j, find b
= 1
b = 8 hrs for Bill alone
:
In the 2nd equation replace b with 8
+ + = 1
+ = 1 -
+ =
Do the same with the 3rd equation
+ + = 1
+ =
use these two equation for elimination
+ +
+ +
----------------------------------Subtraction eliminates j, find m
=
m = 8 hrs for Mike alone
:
find j using eq: + = , replace m with 8
+ =
= -
=
Cross multiply
j = 2*8
j = 16 hrs for Joe alone
:
to do the job alone: m = 8 hrs, j = 16 hrs, b = 8hrs
:
:
Confirm this in the 1st equation
+ + = 1
which is
+ + = 1

RELATED QUESTIONS
Mike, Joe, and Bill are painting a fence. The painting can be finished if Mike and Joe... (answered by ptaylor)

If bill can paint a house in 4 hours and joe can paint a house in 6 hours, how long would (answered by unlockmath,eric.schuh)

Pat and Jane want to paint a fence, pat can paint the fence by himself in 3 hours, jane... (answered by richwmiller,josmiceli)

Bill can mow a lawn in 1 1/2 hours with a riding lawn mower. Joe can mow it in 2 1/2... (answered by unlockmath)

Tom can paint a fence in 5 hours and Huck can paint the same fence in 6 hours. Tom starts (answered by josgarithmetic,ikleyn)

Joe and Renee are building a fence. Joe can build a fence alone in 4 hours. If Renee... (answered by Boreal,josmiceli)

Painting can be done in 8 hours if Jefferson and Pasha work together. How long will it... (answered by ankor@dixie-net.com,greenestamps)

Jonathan can paint a room in 8 hrs. After painting for 2 hours, his brother, David joined (answered by fractalier)

James can paint a room in 4 hours, while Mike can paint the same room in 5 hours. Working (answered by josgarithmetic)