Question 1183745
the formula that i use for problems such as this is:
p * r * t = q
p is the number of people.
r is the average rate that each person works.
t is the time.
q is the quantity.


the implicit assumption is that each person always works at the average rate per person.
that is assumed to be a constant.


in your problem, p * r * t = q becomes:
15 * r * 7 = 6
solve for r to get:
r = 6 / (15 * 7) = 6/105 = .057428571, which i stored in a variable called x.
the formula then becomes:
p * x * t = q
when p = 15 and t = 7, the formula becomes:
15 * x * 7 = q
solve for q to get:
q = 15 * x * 7 = 6.


this confirms the average rate per person is accurate.


when p = 21, the formula becomes:
21 * x * t = 6
solve for t to get:
t = 6 / (21 * x) = 5.


with 15 people working, it takes 7 days.
with 21 people working, it takes 5 days.


if the same quantity has to be done in 2 days, the formula becomes:
p * x * 2 = 6
solve for p to get:
p = 6 / (2 * x) = 52.5 days.


don't forget, .....
x = 6/105 = .0571428571.
that's the average rate per person that is assumed to be a constant.


in real life, it probably is not.