Work Applications

**Work**
problems involve two or more people or machines (etc.) working either
with or against one another to perform a task. Many books use a chart
to organize information into an equation to solve this type of application
problem. There is also a work formula. It may be easier to solve
work problems with this formula.

The formula is simply,
, where a and b are “working alone” times and T is the
working together time.

Problem: Mateo can cut the yard in **
8 hours**, Chet can cut the yard in **
14 hours**, how long will it take to cut the yard if they work
together?

Since **8 hours **
and** 14 hours **are working alone
times, substitute these values into the formula for a and b. Solve
for T.

… LCD (8, 14, T) = 56T … multiply all terms by 56T

7T + 4T = 56

11T = 56

hours