Question

A crew of loggers cleared 1/2 acre of lumber in 4 days. How long will it take the same crew to clear 2 3/4 acres of lumber?

Answer 1

The first think we presume: it is 2 3/4 acres more and does not include the 1/2 acre they have already cleared. 

Then it is a ratio equation problem.  I change fractions to decimal equivalents. 

So you set  0.5 acres / 4 days  and 2.75 acres / n days

Then multiply means and extremes 
4(2.75) = 0.5(n) 
11 = 0.5(n)   divide both sides by 0.5 to get n alone 
11/0.5 = n   solve for n 
22 = n 
It will take the same crew 22 days to clear 2 3/4 more acres. 

Answer 2

Set up a proportion of acres to days. 1/2 acre is to 4 days as 2 3/4 acres is to x days.

x= # days to clear 2 3/4 acres
2 3/4 to improper fraction= 11/4

(1/2)/4 = (11/4)/x
cross multiply

(1/2 * x) = (4 * 11/4)
on the right, the 4 "cancels out"

1/2x= 11
divide both sides by 1/2

x= 11 ÷ 1/2
to divide fractions, multiply by reciprocal/inverse of 1/2

x= 11 * 2/1
x= 22 days

ANSWER: It would take 22 days to clear 2 3/4 acres.

Hope this helps! :)