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Question 587646: mark and matt can do a piece of work in 4 days.mark and mike can do the work in 6 days together.matt and mike together can do it in 5 days. how long would it take each alone to do the work?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! mark and matt can do a piece of work in 4 days.mark and mike can do the work in 6 days together.matt and mike together can do it in 5 days. how long would it take each alone to do the work?
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let x=days mark can do the work alone
1/x =mark's work rate
let y=days matt can do the work alone
1/y =matt's work rate
let z=days mike can do the work alone
1/z =mike's work rate
..
sum of individual work rates=work rate working together
1) 1/x+1/y=1/4
2) 1/x+1/z=1/6
3) 1/y+1/z=1/5
subtract eq3 from eq2, eliminating 1/z
4) 1/x-1/y=1/6-1/5=5/30-6/30=-1/30
add eq1 and eq4, eliminating 1/y
5) 2/x=1/4-1/30=15/60-2/60=13/60
2/x=13/60
x=120/13
..
1) 1/x+1/y=1/4
13/120+1/y=1/4
1/y=1/4-13/120=30/120-13/120=17/120
y=120/17
..
3) 1/y+1/z=1/5
17/120+1/z=1/5
1/z=1/5-17/120=24/120-17/120=7/120
z=120/7
..
ans:
days mark can do the work alone=120/13
days matt can do the work alone=120/17
days mike can do the work alone=120/7
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