Solve each problem. See ExampleEXAMPLESolving a Work Rate ProblemOne printer can do a job...

Solve each problem. See Example

EXAMPLE

Solving a Work Rate Problem

One printer can do a job twice as fast as another. Working together, both printers can do the job in 2 hr. How long would it take each printer, working alone, to do the job?

SOLUTION

Step 1 Read the problem. We must find the time it would take each printer, working alone, to do the job.

Step 2 Assign a variable. Let x represent the number of hours it would take the faster printer, working alone, to do the job. The time for the slower printer to do the job alone is then 2x hours.

Therefore, = the rate of the faster printer ( job per hour)

and = the rate of the slower printer (job per hour).

The time for the printers to do the job together is 2 hr. Multiplying each rate by the time will give the fractional part of the job accomplished by each.

Step 3 Write an equation. The sum of the two parts of the job accomplished is 1, since one whole job is done.

Step 4 Solve.

Step 5 State the answer. The faster printer would take 3 hr to do the job alone, and the slower printer would take 2(3) = 6 hr. Be sure to give both answers here.

Step 6 Check. The answer is reasonable, since the time working together (2 hr, as stated in the problem) is less than the time it would take the faster printer working alone (3 hr, as found in Step 4).

Filling a Pool Suppose Blake discovered his error (see Exercise) after an hour-long surf. If he then closed the outlet pipe, how much more time would be needed to fill the pool?

Filling a Pool An inlet pipe can fill Blake’s pool in 5 hr, while an outlet pipe can empty it in 8 hr. In his haste to surf the Internet, Blake left both pipes open. How long did it take to fill the pool?