SOLUTION: if 10 people made 1 building in 40 days then in how many days will it take 20 people to build the 1 building?

Question 887220: if 10 people made 1 building in 40 days then in how many days will it take 20 people to build the 1 building?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the formula is:
r*p*t = q
r = rate per person
p = number of persons.
t = time in days
q = 1 building

when you have 10 people working on the building and they complete it in 40 days, then the formula becomes:

r * 10 * 40 = 1
solve for r to get r = 1/400

when you have 20 people working at the same rate per person, then the formula becomes:

1/400 * 20 * t = 1
solve for t to get t = 20

you can also solve this as an inverse ratio.
the formula for an inverse ratio is y = k/x.
solve for k in this formula and you get k = y * x.

when you have 10 people working, the building is constructed in 40 days.
y = 40
x = 10
let y = 40 and x = 10 and the formula becomes:
y = k / 10
solve for k to get:
k = 10 * 40 = 400

now that you know the value of k, solve the problem as follows:
y = what you want to find out.
x = 20
k = 400
formula becomes y = 400 / 20 which results in y = 20.

if you did not know that it was an inverse variation type problem, then the first option would have been the way to go.

the basic formula is r*p*t = q
r is the rate per person
p is the number of persons
t is the time
q is the quantity of work produced

since you knew q = 1 building and t = 40 days and p = 10, then you could solve for r.
the formula you used was:
r*10*40 = 1 which resulted in r = 1/400

once you knew r, you could solve for t when p = 20.
the formula you used was:
1/400 * 20 * t = 1 which resulted in t = 20

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