|
Question 1066074: 8 workers can paint a building in 24 days.How many days will 18 workers take to paint the same building
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! this can be an inverse variation type problem.
the formula to use is y = k/x
set y = 24 days and set x = 8 workers and solve for k.
you get 24 = k/8
solve for k to get k = 192
k is the constant of variation and will always remain the same.
when x = 18, the formula becomes y = 192/18.
solve for y to get y = 10 and 2/3 days.
to see if this is correct, use the rate of each person * number of people * time = quantity of work formula.
when people paint 1 building in 24 days, this formula becomes:
r * 8 * 24 = 1
r is the rate of each person.
8 is the number of people.
24 is the number of days.
1 is the quantity of work produced (1 painted building).
solve for r to get r = 1 / (8 * 24)
you get r = 1/192.
when the number of people is 18 and the rate of each person is 1/192, the formula becomes:
1/192 * 18 * t = 1
1/192 is the rate of each person.
this means each person paints 1/192 of the building in one day.
18 is the number of people painting.
t is the number of days
1 is the quantity of work produced (1 painted building).
solve for t to get t = 1 / (18 * 1/192)
simplify to get t = 1 / (18/192)
this is equivalent to t = 1 * 192/18
simplify to get t = 192/18
convert to a mixed fraction to get t = 10 and 2/3 days.
the answer is the same whether you use the inverse variation formula or the rate of each person * number of people * time = quantity of work produced formula.
your solution should be 10 and 2/3 days.
|
|
|
| |
