|
Question 947903: A Certain Job Can Be Done By 8 Men In 20 Days. After 5 Days, 3 Men Left The Job. How Long Would It Take The Remaining Men To Finish The Job?
Found 2 solutions by Theo, Fombitz:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the general formula is:
r*p*t = q
r is the rate that each person works at.
p is the number of persons.
t is the amount time.
q is the quantity of work.
in this problem:
r is what you want to find
p is 8
t is 20 days
q is 1 job
in this problem, r*p*t = q becomes r*8*20 = 1
solve for r to get r = 1/160.
this means that 1 person can complete 1/160 of the job in 1 day.
if you replace r in the equation we just worked, you would get r*p*t = q becomes 1/160 * 8 * 20 = 1 which becomes 160 / 160 = 1 which becomes 1 = 1.
this confirms the solution for r is correct.
not that you know r, you can solve the problem.
you are told that, after 5 days, 3 men left the job.
you can use r and p and t to solve for q.
first you want to find how much of the job was finished by the 8 original men in 5 days.
r*p*t = q becomes 1/160*8*5 = q
solve for q to get q = 40/160 which reduces to 1/4.
8 men will complete 1/4 of the job in 5 days.
that means that 3/4 of the job still remains to be done.
the 8 men are working at the rate of 1/160 of the job per day per person. This rate per person remains constant throughout, regardless of the number of persons working.
3 men leave the job, so you are left with 5 men to complete it.
you want to know how long it will take those 5 men to complete the remaining 3/4 of the job.
the general formula of r*p*t = q becomes 1/160*5*t = 3/4
the rate per person is still the same at 1/160 of the job in one day.
the number of people is now 5.
t is what you want to find.
q is equal to the remaining 3/4 of the job that still needs to be done.
1/160*5*t = 3/4 is the equation you now need to solve for t.
solve for t to get t = 24 days
the remaining 5 people will finish the remaining 3/4 of the job in 24 additional days.
the total number of days to finish the job is therefore 5 + 24 = 29 days.
to confirm, do the following:
the total job required 29 days.
5 days with 8 people working and 24 days with 5 people working.
the rate per person is the same at 1/160 as we had previously calculated.
1/160 * 8 * 5 = 40/160 = 1/4 of the job.
1/160 * 5 * 24 = 120/160 = 12/16 = 3/4 of the job.
1/4 and 3/4 equal the whole job.
the numbers check out and the number of days required for the 5 men to complete the job is 24 days.
Answer by Fombitz(32388)  (Show Source):
|
|
|
| |
