SOLUTION: A wall is built by 17 men in 24 days. In how many days can 18 men do the work if hours per day are reduced in the ratio 5:4?

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Question 764170: A wall is built by 17 men in 24 days. In how many days can 18 men do the work if hours per day are reduced in the ratio 5:4?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
EDIT: previous version had mishandled ratio of old to new hours.

wall is built by 17 men in 24 days.
If just 1 man, then need 17 times more days.
1 wall built per 17%2A24 days for just one man working.
ONE MAN RATE: 1%2F%2817%2A24%29 jobs per day.

If hours per workday are unchanged, then 18 men would use the rate of 18%281%2F%2817%2A24%29%29 jobs per day.
That is 18%2F%2817%2A24%29 jobs per day.

Shortening the hour per workday by factor of 4%2F5 would mean more time, as days, needed to do the job:
Rate for the 18 men then needs to be %284%2F5%29%2818%2F%2817%2A24%29%29 jobs per day.
%284%2A18%29%2F%285%2A17%2A24%29=
.
highlight%2828%261%2F3%29 days for one job.


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Just as easy or easier to skip the 0.05514 and just taken the rate as 16%2A17%2F15, and then did the computation to 18%264%2F30 days per job.