SOLUTION: A vineyard’s grapes can be harvested by 10 workers in 5 hours. If one worker starts the harvest at noon, and another worker joins the harvest each hour on the hour, at what time

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A vineyard’s grapes can be harvested by 10 workers in 5 hours. If one worker starts the harvest at noon, and another worker joins the harvest each hour on the hour, at what time      Log On


   

Question 948439: A vineyard’s grapes can be harvested by 10 workers in 5 hours. If one worker starts the
harvest at noon, and another worker joins the harvest each hour on the hour, at what time
will the harvest be completed?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
r, rate for one worker.
10r%2A5=1, the one job of THE VINEYARDS GRAPES.
r=1%2F50.

First hour, 1%2Ar%2A1=%281%2F50%29, a small amount of the job done.
Hour Number Two, two workers, when completed time:
%281%2F50%29%2A1%2B%282%2F50%29%2A1
Hour Number Three, three workers, when completed time:
1%2F50%2B2%2F50%2B%283%2F50%29%2A1

UNKNOWN number of hours completed, for finishing harvesting the vineyard's grapes:
(1/50)(1+2+3+...n)=1

1+2+3+...n=50

OR in renderable notational form
sum%28x%2Ci=1%2Cn%29=50

%28n%2F2%29%281%2Bn%29=50

n%281%2Bn%29=100

n%5E2%2Bn=100

n%5E2%2Bn-100=0

n=%28-1%2B-+sqrt%281%2B4%2A100%29%29%2F2

n=%28-1%2Bsqrt%28501%29%29%2F2
n=10.69, more than ten hours but less than eleven hours.
The actual time from start to finish would be 10 hours 41 minutes.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

A vineyard’s grapes can be harvested by 10 workers in 5 hours. If one worker starts the
harvest at noon, and another worker joins the harvest each hour on the hour, at what time
will the harvest be completed?
Time taken to do entire job: 12 hours

Time job completed: highlight_green%28system%2812%3A00_AM_or%2Cmidnight%29%29