SECTION 7.5 Applications of Rational Expressions 401
Part done part done 1 whole
by Kareem by Letitia is job.1
Multiply by the LCD, 35.Distributive property
Combine like terms.Divide by 12.Working together, Kareem and Letitia can do the job in or 2 hr, 55 min. Check
this result in the original problem. NOW TRY
3512 hr,
x=
35
12
12 x= 35
5 x+ 7 x= 35
35 a
1
7
x+
1
5
xb = 35 # 1
=
1
5
+ x
1
7
x
+To solve a work problem, we use this fact to express all rates of work.
Time Working Fractional Part
Rate Together of the Job DoneKareem xLetitia x
1
5 x1
51
7(^1) x
7
OBJECTIVE 5 Solve applications about work rates.
People work at different rates. If the letters r, t, and Arepresent the rate at which
work is done, the time required, and the amount of work accomplished, respec-
tively, then Notice the similarity to the distance formula,
Amount of work can be measured in terms of jobs accomplished. Thus, if
1 job is completed, then and the formula gives the rate as
,or r=
1
t
1 = rt.
A= 1,
Art. d=rt.
PROBLEM-SOLVING HINT
Rate of WorkIf a job can be accomplished in tunits of time, then the rate of work is
1
t
job per unit of time.
Solving a Problem about WorkLetitia and Kareem are working on a neighborhood cleanup. Kareem can clean up all
the trash in the area in 7 hr, while Letitia can do the same job in 5 hr. How long will
it take them if they work together?
Let the number of hours it will take the two people working together.
We use Since the rate for each person will be where tis the time
it takes the person to complete the job alone. Kareem can clean up all the trash in 7 hr,
so his rate is of the job per hour. Similarly, Letitia’s rate is of the job per hour.^1715
1A= rt. A= 1, t,
x=
EXAMPLE 8
Together they complete 1 job.
The sum of the fractional parts
should equal 1.⎧⎪⎨⎪⎩ ⎧⎪⎨⎪⎩ ⎧⎪⎨⎪⎩
NOW TRY
EXERCISE 8
Using her zero-turn riding lawn
mower, Gina can mow her lawn
in 2 hr. Using a traditional
mower, Matt can mow the same
lawn in 3 hr. How long will it
take them to mow the lawn
working together?
NOW TRY ANSWER
8.^65 hr, or 1 hr, 12 min