Question 964905
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.