SOLUTION: 8 workers can paint a building in 24 days.How many days will 18 workers take to paint the same building

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.

RELATED QUESTIONS
8 workers can paint a building in 24 days . How many days will 18 workers take to paint... (answered by bdolan911)

It takes 24 days for 8 workers to complete painting a building, how many days will it... (answered by josgarithmetic)

Ten workers can paint a house in six days. Working at the same rate, how many days will... (answered by Alan3354)

If 15 workers can paint 18 houses in 24 days, how many days will 40 workers take to paint (answered by stanbon)

If 15 workers can paint a certain number of houses in 24 days, how many days will 40... (answered by fractalier)

if 3 workers can finish painting a house in 2 days, how many days will it take 6 workers (answered by josgarithmetic,josmiceli,ikleyn)

three workers can paint a house in 14 days. assuming that the workers work at the same... (answered by josmiceli)

Five workers paint four houses in six days. Working at the same rate as these workers,... (answered by promotion analysis,ankor@dixie-net.com)

If it takes 6 workers to paint a room in 14 days, how many workers does it take to paint... (answered by checkley71)