Chapter 8 linear appliCaTionS 279EXAMPLE
Jerry needs 40 minutes to mow the lawn. Lou can mow the same lawn in
30 minutes. If Jerry works alone for 10 minutes then Lou joins in, how long
will it take for them to finish the job?
Because Jerry worked for 10 minutes, he did^1040 = 41 of the job alone. So,
there is 1 – ^14 = ^34 of the job remaining when Lou started working. Let t
represent the number of minutes they worked together—after Lou joins
in. Even though Lou does not work the entire job, his rate is still 301.
Worker Quantity Rate Time
Jerry 1 1/40 40
Lou 1 1/30 30
Together 3/4 34 3
tt 4= tThe equation to solve is^1
40
+ ^1
30= ^3
4
t. The LCD is 120t.
1
401
303
4
120 1
401
30120 3
4
120 1+=
+
=
t
tt
t
t
440120 1
30903490
790
90
7
+
=+=
=
=ttt
t
tTogether, they will work^907 = 1276 minutes.
Pipe I can fill a reservoir in 6 hours. Pipe II can fill the same reservoir in
4 hours. If Pipe II is used alone for 221 hours, then Pipe I joins in to finish the
job, how long will the first pipe be used?
The amount of time Pipe I is used is the same as the amount of time both
pipes work together. Let t represent the number of hours both pipes are
used. Alone, Pipe II performed 221 parts of a 4-part job:
2
45
24 5
21
45
81 5
83
8(^12)
=÷=⋅=−,so =
EXAMPLE
Jerry needs 40 minutes to mow the lawn. Lou can mow the same lawn in