SOLUTION: M can do a piece of work in 4 hours, N and P together in 3 hours, and M and P together in 2 hours. How long will N alone take to do it?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: M can do a piece of work in 4 hours, N and P together in 3 hours, and M and P together in 2 hours. How long will N alone take to do it?      Log On


   



Question 947130: M can do a piece of work in 4 hours, N and P together in 3 hours, and M and P together in 2 hours. How long will N alone take to do it?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Rate x Time = Output
Let's choose the output to be 100%.
R%5Bm%5D%2A4=100
1.R%5Bm%5D=25
.
.
%28R%5Bn%5D%2BR%5Bp%5D%29%2A3=100
2.R%5Bn%5D%2BR%5Bp%5D=100%2F3
.
.
%28R%5Bm%5D%2BR%5Bp%5D%29%2A2=100
3.R%5Bm%5D%2BR%5Bp%5D=50
Substitute eq. 1 into eq. 3,
25%2BR%5Bp%5D=50
R%5Bp%5D=25
Now substitute this into eq. 2,
R%5Bn%5D%2B25=100%2F3
R%5Bn%5D=100%2F3-75%2F3
R%5Bn%5D=25%2F3
So then,
R%5Bn%5D%2At%5Bn%5D=100
%2825%2F3%29%2At%5Bn%5D=100
t%5Bn%5D=12hrs