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

Answer:

26.67 hours or 26 hours and 40 minutes.

Step-by-step 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:

$B = \frac{10\ ft}{4 h} \\B = 2.5\frac{\ ft}{h}$

Joe:

$B = \frac{10\ ft}{5 h} \\B = 2.0\frac{\ ft}{h}$

Their combined work rate is:

$W =J+B\\W = 2.5\frac{\ ft}{h}+2.0\frac{\ ft}{h}\\W=4.5\frac{\ ft}{h}$

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

$t = \frac{120\ ft}{2.5\frac{\ ft}{h}} \\t= 26.67\ h$