SOLUTION: 3 boys are working on a school project. Joseph and Bill can finish the prohectbin 10 days. Bill and Elmer can finish it in 12 days. Joseph and Elmer can finish it in 15 days. If ea

Algebra ->  Rate-of-work-word-problems -> SOLUTION: 3 boys are working on a school project. Joseph and Bill can finish the prohectbin 10 days. Bill and Elmer can finish it in 12 days. Joseph and Elmer can finish it in 15 days. If ea      Log On


   

Question 1146303: 3 boys are working on a school project. Joseph and Bill can finish the prohectbin 10 days. Bill and Elmer can finish it in 12 days. Joseph and Elmer can finish it in 15 days. If each boy works alone, how long will it take him to finish the project?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Each boy's RATE:
x, y, z for Joseph, Bill, Elmer

system%28x%2By=1%2F10%2Cy%2Bz=1%2F12%2Cx%2Bz=1%2F15%29

x%2By%2By%2Bz%2Bx%2Bz=1%2F10%2B1%2F12%2B1%2F15
2x%2B2y%2B2z=6%2F60%2B5%2F60%2B4%2F60
2x%2B2y%2B2z=15%2F60
2%28x%2By%2Bz%29=1%2F4
x%2By%2Bz=1%2F8
-
x%2By%2Bz-%28y%2Bz%29=1%2F8-1%2F12---------this will give value for x, a rate for Joseph; from which you want its reciprocal.

The other two are done similarly.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Here is an alternative to the standard method shown by the other tutor for solving "working together" problems. Many students like this method because it avoids working with those fractions.

Assume it is sensible for the "job" to be done multiple times; then consider the least common multiple of the given times. The LCM of 10, 12, and 15 is 60. So how many of these jobs can each combination of boys do in 60 days?

Joseph and Bill in 60 days can do 60/10 = 6 of these jobs.
Bill and Elmer in 60 days can do 60/12 = 5 of these jobs.
Elmer and Joseph in 60 days can do 60/15 = 4 of these jobs.

So write equations for the numbers of jobs each combination of boys can do in 60 days:

(1) J+B = 6
(2) B+E = 5
(3) E+J = 4

Add the three equations and simplify:

(4) J+B+E = 7.5

Now compare (4) with each of (1), (2), and (3):

E = 7.5-6 = 1.5
J = 7.5-5 = 2.5
B = 7.5-4 = 3.5

Elmer alone can do 1.5 of these jobs is 60 days; so working alone he can complete one job in 60/1.5 = 40 days.

Joseph alone can do 2.5 of these jobs in 60 days; so working alone he can complete one job in 60/2.5 = 24 days.

Bill alone can do 3.5 of these jobs in 60 days; so working alone he can complete one job in 60/3.5 = 120/7 = 17 1/7 days.

ANSWERS:
Elmer: 40 days
Joseph: 24 days
Bill: 17 1/7 days