SOLUTION: If 12 men and 16 boys can do a piece of work in 5 days and 13 men and 24 boys can do the same piece of work in 4 days. How long will 7 men and 10 boys take to complete the same wo

Algebra ->  Rate-of-work-word-problems -> SOLUTION: If 12 men and 16 boys can do a piece of work in 5 days and 13 men and 24 boys can do the same piece of work in 4 days. How long will 7 men and 10 boys take to complete the same wo      Log On


   

Question 616507: If 12 men and 16 boys can do a piece of work in 5 days and 13 men and 24 boys can do the same piece of work in 4 days. How long will 7 men and 10 boys take to complete the same work?

Found 2 solutions by ankor@dixie-net.com, kamallohia:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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f 12 men and 16 boys can do a piece of work in 5 days and
13men and 24 boys can do the same piece of work in 4 days.
how long will 7 men and 10 boys take to complete the same work?
:
Let b = days required for one boy to do the job
Let m = days required for one man to do the job
Let the completed job = 1
:
"If 12 men and 16 boys can do a piece of work in 5 days"
%2812%285%29%29%2Fm + %2816%285%29%29%2Fb = 1
60%2Fm + 80%2Fb = 1
:
"13men and 24 boys can do the same piece of work in 4 days."
%2813%284%29%29%2Fm + %2824%284%29%29%2Fb = 1
52%2Fm + 96%2Fb = 1
:
We can combine the two equations
60%2Fm + 80%2Fb = 52%2Fm + 96%2Fb
combine like terms
60%2Fm - 52%2Fm = 96%2Fb - 80%2Fb
8%2Fm = 16%2Fb
cross multiply
8b = 16m
divide by 8
b = 2m
:
Use the 1st scenario equation to find m, replace b with 2m
60%2Fm + 80%2F%282m%29 = 1
reduce the fraction
60%2Fm + 40%2Fm = 1
Multiply by m
60+40 = m
m = 100 days for one man to do the job
then
b = 2(100)
b = 200 days for one boy to do the job
:
" how long will 7men and 10 boys take to complete the same work?
let t = time required for this to happen
%287t%29%2F100 + %2810t%29%2F200 = 1
reduce the fraction, to give us a common denominator
%287t%29%2F100 + 5t%2F100 = 1
mult by 100
7t + 5t = 100
12t = 100
t = 100/12
t = 81%2F3 days for 7 men and 10 boys to do the job

Answer by kamallohia(18) About Me  (Show Source):
You can put this solution on YOUR website!
Ans: 8 and 1/3 days
Sol: Let a man's daily work is x units and that of a boy is y units.
So total amount of work, W = 5(12x + 16y) = 4(13x + 24y)
=> 60x + 80y = 52x + 96y
=> 8x = 16y
=> x = 2y i.e. W = 5(24y + 16y) = 200y.
Now 7men and 10 boys' work of a day is = 7x + 10y = 14y + 10y = 24y.
So total days required to finish the work is = 200y/24y = 25/3 = 8 and 1/3 days.