SOLUTION: 40 men can complete a work in 40 days. they started the work together. but at the end of each 10th day 5men left the job the work would have been completed in

Algebra ->  Test -> SOLUTION: 40 men can complete a work in 40 days. they started the work together. but at the end of each 10th day 5men left the job the work would have been completed in      Log On


   

Question 1030927: 40 men can complete a work in 40 days. they started the work together. but at the end of each 10th day 5men left the job the work would have been completed in
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The question is not clear; but still what is unknown in the description can be solved.

First sentence:
40%2Ar%2A40=1, because the rate for the fourty men is 40r, and the ONE "work" would be done in 40 days.

What should be the second sentence composed of two periods of time:
40r%2A10%2B%2840-5%29r%2Ax=1, because the men working in the two time periods of 10 days and x days would do ONE "work". Notice the 40-5 for the number of workers for the time period of x days. That is 35 men working for x days.
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Solve this equation for x.
400r%2B35rx=1
35rx=1-400r
highlight_green%28x=%281-400r%29%2F%2835r%29%29-------very important but not yet the finished formula.
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The question to ask should be like, how many days after the 5 men leave the group do the remaining men finish the job?


Look at the first equation now.
40r%2A40=1
40%5E2%2Ar=1
r=1%2F1600-------this is the ONE MAN work rate. Substitute this into the green-outlined formula for x. Evaluate.

x=%281-400%281%2F1600%29%29%2F%2835%281%2F1600%29%29

x=%281-1%2F4%29%2F%2835%2F1600%29

x=%283%2F4%29%281600%2F35%29
x=%283%2A4%2A4%2A100%29%2F%284%2A7%2A5%29

x=%283%2A4%2A20%29%2F7
x=240%2F7

Looks like highlight%28x=34%262%2F7%29, a fraction of a day more than 34 days.