Algebra Demystified 2nd Ed

Chapter 8 linear appliCaTionS 283

2360

560

60

5

12

tt

t

t

+=

=

==

It will take Scott and Neil 12 minutes to finish painting the wall.

2. Hose 2 is used alone for 164 = 41 of the job, so 1 −=^1434 of the job remains.

Let t represent the number of minutes both hoses will be used.

Worker Quantity Rate Time

Hose 1 1 1/20 20

Hose 2 1 1/16 16

Together 3/4 3

4

34 3

4

t

tt=

t

The equation to solve is 201 += 161 43 t. The LCD is 80t.

1

20

1

16

3

4

80 1

20

1

16

80 3

4

80 1

20

+=

+











= 









t

tt

t

t







+ 







=

+=

=

==

80 1

16

60

4560

960

60

9

(^623)
t
tt
t
t
Both hoses will be used for 623 minutes or 6 minutes 40 seconds. There-
fore, Hose 1 will be used for^623 minutes.

3. Some of the information given in this problem is given in hours and
   other information in minutes. We must use only one unit of measure.
   Using minutes as the unit of measure will make the computations a little
   less messy. Let t represent the number of minutes both Sarah and
   Jeremy work together. Alone, Jeremy completed^2060 =^13 of the job,
   so^1 −= 31 23 of the job remains to be done.