SOLUTION: If 6 masons and 8 helpers can do a construct a boundary wall in 10 days while 26 masons and 48 helpers can do the same in 2 days, what is the time taken by 15 masons and 20 help

Algebra ->  Rate-of-work-word-problems -> SOLUTION: If 6 masons and 8 helpers can do a construct a boundary wall in 10 days while 26 masons and 48 helpers can do the same in 2 days, what is the time taken by 15 masons and 20 help      Log On


   

Question 1125786: If 6 masons and 8 helpers can do a construct a boundary wall in 10 days while 26
masons and 48 helpers can do the same in 2 days, what is the time taken by 15
masons and 20 helpers to do the same work?
a. 4 days
b. 5 days
c. 6 days
d. 7 days
Answer by ikleyn(52748) About Me  (Show Source):
You can put this solution on YOUR website!
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We are given that


 6m +  8h = 1%2F10    (1)
26m + 48h = 1%2F2     (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 = %281%2A96+-+1%2A80%29%2F%2860%2A96-52%2A80%29 = 16%2F%28%2860%2A6-52%2A5%29%2A16%29 = 1%2F%2860%2A6-52%2A5%29 = 1%2F%28360-260%29 = 1%2F100 = 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%2F8 = 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.

Solved.

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