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 1045208: 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, ikleyn, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Alternative method is assign variables for each type of person's rate in units of JOB/DAYS, and this gives linear equations.

x for one-boy rate
y for one-man rate

system%28%282y%2B5x%294=1%2C%284y%2B4x%293=1%29

system%2820x%2B8y=1%2C12x%2B12y=1%29


Elimination Method should be more comfortable to use for solving the system.
Multiply first equation by 3, and multiply second equation by 2.
-
system%2860x%2B24y=3%2C24x%2B24y=2%29
-
Subtract second equation from first equation, member by member.
system%28%2860x%2B24y%29-%2824x%2B24y%29=3-2%29
36x=1
highlight%28x=1%2F36%29
Remember, here the unit of work rate is JOBS%2FDAYS, so this rate for ONE BOY means "ONE JOB done in 36 DAYS".

You can use the same method for eliminating the x; but here, the best choice is return to system%2820x%2B8y=1%2C12x%2B12y=1%29, but multiply first equation by 3; and multiply second equation by 5.
.
.
You do it......

Answer by ikleyn(52810) About Me  (Show Source):
You can put this solution on YOUR website!
.
See the lesson
    - Solving rate of work problem by reducing to a system of linear equations,
in this site.

You will find there other similar solved problems with detailed solutions.


Answer by MathTherapy(10555) 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?
Isn't this the same as: Linear_Equations_And_Systems_Word_Problems/1045207?

Why did you post it twice? Oh, I see. Maybe because you got an answer that was nowhere near the correct one. Okay! 

The correct answer is there now, so you can revisit that problem.