SOLUTION: Danielle can complete a project in twelve days and Mackenzie can do the same project in forty-eight days. Danielle worked on the project alone for four days before Mackenzie joined

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Danielle can complete a project in twelve days and Mackenzie can do the same project in forty-eight days. Danielle worked on the project alone for four days before Mackenzie joined      Log On


   

Question 768474: Danielle can complete a project in twelve days and Mackenzie can do the same project in forty-eight days. Danielle worked on the project alone for four days before Mackenzie joined her. How many days did Mackenzie work on the project until it was done?

Found 2 solutions by josgarithmetic, ankor@dixie-net.com:
Answer by josgarithmetic(39623) About Me  (Show Source):
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Danielle's rate: 1%2F12 job per day
MacKenzie's rate: 1%2F48 job per day
Their combined rate: 1%2F12%2B1%2F48=5%2F48 job per day
Basically r*d=j ----------- r is rate, d is days, j is job quantity

Danielle alone, 4 days.
%281%2F24%29%2A4

MacKz joined Danielle, d days, unknown.
%285%2F48%29%2Ad

The project or job was done in 4+d days.
highlight%28%281%2F24%29%2A4%2B%285%2F48%29%2Ad=1%29
SOLVE FOR d.

To begin the symbolic solving,
48%281%2F24%29%2A4%2B48%285%2F48%29%2Ad=48
2%2A4%2B5d=48
5d=48-8=40
highlight%28d=8%29_____________________so actually finished solution.
8 days to finish with MacKenzie.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Danielle can complete a project in twelve days and Mackenzie can do the same project in forty-eight days.
Danielle worked on the project alone for four days before Mackenzie joined her.
How many days did Mackenzie work on the project until it was done?
:
Let m = no. of days that M worked to complete the job with D
then
(m+4) = no. of days worked by D
;
Let the completed jobe = 1
:
the shared work equation
%28m%2B4%29%2F12 + m%2F48 = 1
Clear the denominators, by multiplying by 48, resulting in:
4(m+4) + m = 48
4m + 16 + m = 48
5m = 48 - 16
m = 32/5
m = 6.4 days worked by M
:
:
We can confirm this by finding what fraction of the job each worked
the two fraction should add up to 1, (D worked 10.4 days)
10.4/12 = .867
6.4/48 = .133
---------------
total to: 1.00