One house was built in 66 days by 12 workers. How many days would it take to build a similar house with 44 workers?

Answer 1

66 days to build a house by 12 workers

how much less time would it take to build the same house with 44 workers?

there's an inverse relationship between number of workers, W, and time in days, D

66 =k/W = k/12

k = 66(12) = 792

D= 792/W

D = 792/12 = 18 days for 44 workers

check the solution:

24 workers would do it in 33 days, half the time, with twice as many workers

48 workers would do it in 33/2 = 16 1/2 days, 1/4 the time with 4 times as many workers

44 workers would do it in a little more than 16 1/2 days, with 4 less workers than 48

maybe about 17 or 18 days

4 workers would take 66x3 = 198 days, 1/3 as many workers as 12 workers. 4/12 = 1/3

1/16.5 - 1/198= 1/D where D = the number of days it takes 44 workers

multiply both sides by (16.5)(198)D

198D - 16.5D = 16.5(198)

181.5D = 3267

D = 3267/181 = 18 days for 44 workers