SOLUTION: 25 men working 8 hours a day plant trees on a forest plot in 63 days. Calculate the number of days 45 men working 7 hours a day would take to plant that same number of trees.

Algebra ->  Rate-of-work-word-problems -> SOLUTION: 25 men working 8 hours a day plant trees on a forest plot in 63 days. Calculate the number of days 45 men working 7 hours a day would take to plant that same number of trees.      Log On


   

Question 764891: 25 men working 8 hours a day plant trees on a forest plot in 63 days. Calculate the number of days 45 men working 7 hours a day would take to plant that same number of trees.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
First find how many days the 25 men need if THEIR shift length is 7 hours per day instead of 8 hours per day. Now the 25 men need more days, right? How many days for this job?

25 men ---- 8%2F8 hour for 63%2A8 days
25 men ----%288%2F8%29%2A7 hour for %2863%2A8%29%2F7 days
That is equivalent then to
25 men ----7 hours per day for 72 days.

Next, focus on 1 man instead of 25 men, and look at "days" and not worry about hours (because the hours is now already taken care for ).

If 25 men do the assigned quantity of trees in 72 days, the
ONE man does the trees in 72%2A25 days.
This one-man rate is highlight%281%2F%2872%2A25%29%29 job per day.

Last, the rates of the men working together are additive, so for 45 men, now understood to work in shifts per day of 7 hours, the number of days, using the variable d, to do this tree planting job is:
45%2A%281%2F%2872%2A25%29%29%2Ad=1
Although you can simply focus on the group rate for these 45 men:
45%2A%281%2F%2872%2A25%29%29 JOB per DAY, and since you want DAYS per JOB, just use the reciprocal:
highlight%28%2872%2A25%29%2F45%29 DAYS per JOB at 7 hours per day.