Question

40 POINTS PLEASE HELP Joe and Bill are working on building a stone wall that will be 120 feet long. Joe works from one end and is able to build one ten foot section in 5 hours. Bill starts from the other end and is able to finish a ten foot section in 4 hours. How long will it take Joe and Bill to finish building the wall?

Answer 1

26.67 hours or 26 hours and 40 minutes.

Explanation:

To find out how long will it take for Joe and Bill to finish building the wall together, first find their individual work rates in feet per hour:

Bill:

`B = (10\ ft)/(4 h) \\B = 2.5(\ ft)/(h)`

Joe:

`B = (10\ ft)/(5 h) \\B = 2.0(\ ft)/(h)`

Their combined work rate is:

`W =J+B\\W = 2.5(\ ft)/(h)+2.0(\ ft)/(h)\\W=4.5(\ ft)/(h)`

Then, divide the total size of the wall by their work rate to find the time spent to finish it:

`t = (120\ ft)/(2.5(\ ft)/(h)) \\t= 26.67\ h`