Question 1125786
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<pre>
We are given that


 6m +  8h = {{{1/10}}}    (1)
26m + 48h = {{{1/2}}}     (2)


where m is the mason's rate of work and h is the helper's rate of work.


Equivalently


60m + 80h = 1,
52m + 96h = 1.


Solve using the determinant method


m = {{{(1*96 - 1*80)/(60*96-52*80)}}} = {{{16/((60*6-52*5)*16)}}} = {{{1/(60*6-52*5)}}} = {{{1/(360-260)}}} = {{{1/100}}} = 0.01  is the rate of work of one mason.


Then from (1),  8h = 0.1 - 6m = 0.1 - 0.06 = 0.04  ====>  h = {{{0.04/8}}} = 0.005  is the rate of work of one helper.


Now, rate of work of 15 masons PLUS 20 helpers is  15*0.01 + 20*0.005 = 0.25,

so they will complete the job in 4 days.
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Solved.


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You can find many similar solved problems in the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Solving-rate-of-work-problem-by-reducing-to-a-system-of-linear-equations.lesson>Solving rate of work problem by reducing to a system of linear equations</A>,

in this site.