SOLUTION: 2 men and 5 boys can do a piece of work in 4 days, while 4 men and 4 boys can do it in 3 days how long would it take one man alone to do it and how many days would it take one boy

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: 2 men and 5 boys can do a piece of work in 4 days, while 4 men and 4 boys can do it in 3 days how long would it take one man alone to do it and how many days would it take one boy       Log On


   

Question 1045207: 2 men and 5 boys can do a piece of work in 4 days, while 4 men and 4 boys can do it in 3 days how long would it take one man alone to do it and how many days would it take one boy alone to do it?
Found 3 solutions by josgarithmetic, MathTherapy, ikleyn:
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
Time for 1 man to do 1 job, m
time for 1 boy to do 1 job, b

R*T=J rule that relates rate, time, amount of job or amount of work

system%28%282%2Fm%2B5%2Fb%294=1%2C%284%2Fm%2B4%2Fb%293=1%29
Not a linear system, but two equations in two unknown variables.

system%288b%2B20m=bm%2C12b%2B12m=bm%29


Use substitution to solve.

Pick an equation and solve for a variable.
8b-bm%2B20m=0
8b-bm=-20m
b%288-m%29=-20m
b=-20m%2F%288-m%29
b=20m%2F%28m-8%29

Substitute this formula into the other equation.
12%2820m%2F%28m-8%29%29%2B12m=%2820m%2F%28m-8%29%29m
240m%2F%28m-8%29%2B12m=20m%5E2%2F%28m-8%29

240m%2B12m%28m-8%29=20m%5E2

Divide left and right by 4
60m%2B3m%28m-8%29=5m%5E2

60m%2B3m%5E2-24=5m%5E2

60m-24=2m%5E2

2m%5E2-60m%2B24=0

Divide left and right by 2
highlight_green%28m%5E2-30m%2B12=0%29

m=%2830%2B-+sqrt%2830%5E2-4%2A12%29%29%2F2

m=%2830%2B-+sqrt%28900-48%29%29%2F2

m=%2830%2Bsqrt%28852%29%29%2F2-----

m=%2830%2B-+2%2Asqrt%28213%29%29%2F2

m=15%2Bsqrt%28213%29--------time for one man ?

Answer by MathTherapy(10550) About Me  (Show Source):
You can put this solution on YOUR website!

2 men and 5 boys can do a piece of work in 4 days, while 4 men and 4 boys can do it in 3 days how long would it take one man alone to do it and how many days would it take one boy alone to do it?

Answer by ikleyn(52767) About Me  (Show Source):
You can put this solution on YOUR website!
.
Did you see the method and the approach the tutor " josgarithmetic" applied in his solution?

Never apply it for such problems.

There are much more simple and robastic method and approach for it.
See the lesson
    - Solving rate of work problem by reducing to a system of linear equations
in this site.

Every problem of this lesson is an exact analogue to your problem and can serve as a sample to you.
Read them attentively and then solve your problem by substituting your data.

The major idea is: for such problem use "the rate of work" for each participant as basic unknown variables/quantities.

Write the system of equations for these variables.
Usually these systems are simple and easy to solve.

When you solve for the "the rate of work" unknowns, you can easily complete the solution and answer the question.

There is an entire bunch of various rate-of-work problems in this site
    - Rate of work problems,
    - Using Fractions to solve word problems on joint work,
    - Solving more complicated word problems on joint work,
    - Using quadratic equations to solve word problems on joint work,
    - Solving rate of work problem by reducing to a system of linear equations,
    - Selected joint-work word problems from the archive
    - Joint work word problem for the day of April, 1
    - Joint-work problems for 3 participants.

Read them and become an expert in solution joint-work problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.