SOLUTION: 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?

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): You can put this solution on YOUR website!
Rate*Time=Output
Assume each man works at the rate, R.

So then after three days the amount of output is,

So the amount of output that remains to be done is,

So now only 5 men working to output the remaining 85,

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