59. Filling a fountain. Pete’s fountain can be filled using a pipe or a hose. The fountain can be filled using the pipe in 6 hours or the hose in 12 hours. How long will it take to fill the fountain using both the pipe and the hose?
60. Mowing a lawn. Albert can mow a lawn in 40 minutes, while his cousin Vinnie can mow the same lawn in one hour. How long would it take to mow the lawn if Albert and Vinnie work together?
61.
Printing a report.
Debra plans to use two computers to
print all of the copies of the annual report that are needed
for the year-end meeting. The new computer can do the
whole job in 2 hours while the old computer can do the
whole job in 3 hours. How long will it take to get the job
done using both computers simultaneously?
62. Installing a dishwasher. A plumber can install a dishwasher in 50 min. If the plumber brings his apprentice to help, the job takes 40 minutes. How long would it take the apprentice working alone to install the dishwasher?
63. Filling a tub. Using the hot and cold water faucets together, a bathtub fills in 8 minutes. Using the hot water faucet alone, the tub fills in 12 minutes. How long does it take to fill the tub using only the cold water faucet?
64.
Filling a tank.
A water tank has an inlet pipe and a drain
pipe. A full tank can be emptied in 30 minutes if the drain
is opened and an empty tank can be filled in 45 minutes
with the inlet pipe opened. If both pipes are accidentally
opened when the tank is full, then how long will it take to
empty the tank?

6-67
Chapter 6
Summary
447
Wrap-Up±
6
Examples
x
1
(
x
�
3)
x
3
x
1
y
x
3
8
x
+
2
2(4
x
+
1)
4
x
+
1
4
x
2(2
x
)
2
x
7
2
x
x
1
2
x
5
5
3
x
x
x
Examples
3
6
18
x
3
x
5
x
8
a
5
a
x
9
ax
6
x
3
x
9
x
3
5
5
Examples
8, 12
LCD
24
4
ab
3
, 6
a
2
b
4
ab
3
2
2
ab
3
6
a
2
b
2
3
a
2
b
2
b
3
2
b
3
LCD
2
2
3
a
12
a
2
x
7
x
9
x
+
x
3
x
3
x
3
2
1
6
1
7
+
+
x
3
x
3
x
3
x
3
x
Summary
Rational Expressions
Rational expression
Rational Function
Rule for reducing
rational expressions
Least common
denominator
Finding the least
common
denominator
Addition and
subtraction of
rational expressions
The ratio of two polynomials with the
denominator not equal to 0
If a rational expression is used to determine
y
from
x
, then
y
is a rational function of
x
.
If
a
�
0 and
c
�
0, then
ab
b
.
ac
c
(Divide out the common factors.)
Multiplication and Division of Rational Expressions
Multiplication
If
b
�
0 and
d
�
0, then
a
b d
c
b
a
d
c
.
Division
If
b
�
0,
c
�
0, and
d
�
0, then
a
b
(Invert the divisor and multiply.)
d
c
a
b
d
c
.
Addition and Subtraction of Rational Expressions
The LCD of a group of denominators is the
smallest number that is a multiple of all
of them.
1. Factor each denominator completely. Use
exponent notation for repeated factors.
2. Write the product of all of the different
factors that appear in the denominators.
3. On each factor, use the highest power that
appears on that factor in any of the
denominators.

#### You've reached the end of your free preview.

Want to read all 76 pages?

- Spring '13
- c
- Rational Expressions, Fractions, Fraction, Elementary arithmetic, Greatest common divisor, Division of Rational