SOLUTION: If 20 men can complete a piece of job in 8days, how long will it take 10 men to finish the job working at the same rate

Question 964905: If 20 men can complete a piece of job in 8days, how long will it take 10 men to finish the job working at the same rate
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
this is an inverse ratio type problem.
it is also a rate per person * number of people * time = quantity type problem.
you can solve it either way.

with inverse ratio, you will get:

y = k/x is the standard inverse ratio formula.

when y = 8 days, x = 20 men.

use the formula to compute k.

you will get 8 = k/20

solve for k to get:

k = 20*8 = 160

k remains constant.

when x = 10 men, the formula becomes:

y = 160 / 10 which becomes:

y = 16 days.

this stands to reason.

half the men should take twice as long and they do.

now solve using the rate per person * number of people * time = quantity formula.

that formula is abbreviated as r * p * t = q

20 men can finish the job in 10 days.

rate per person is to be calculated using 20 people and 8 days and a quantity of 1 job.

the formula becomes r * 20 * 8 = 1

solve for r to get 4 = 1/(20*8) = 1/160

each person can complete 1/160 of the job in 1 day.

does that make sense?

20 people working at the individual rate of 1/160 of the job in 1 day and taking 8 days would complete 1/160 * 20 * 8 = 1/160 * 160 = 160/160 of the job which is equal to 1 job.

so we have r = 1/160 of the job in one day per person.

use that formula to figure out the time required to do one job if only 10 people were working.

you get r*p*t = q becomes:

1/160 * 10 * t = 1

solve for t to get:

t = 1 / (1/160 * 10) which becomes:

t = 1 / (1/16) which becomes:

t = 1 * (16/1) which becomes:

t = 16

both formulas get you the same answer.

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