WORD PROBLEM PRACTICE:
Section: 7.2
Section: 7.5
1.
You can clean the gutters of your house in 5 hours. Working together, you and your friend can clean the gutters
in 3 hours. Let t be the time (in hours) your friend would take to clean the gutters when working alone. Write and solve
an equation to find how long your friend would take to clean the gutters when working alone.
 Hint: Work done  Work rate  Time
You can kayak around a certain island in 3 hours. Kayaking together, you and your friend can kayak around the
island in 1.4 hours. Let t be the time (in hours) your friend would take to kayak around the island when kayaking alone.
Write and solve an equation to find how long your friend would take to kayak around the island when kayaking alone.
 Hint: Work done  Work rate  Time
2.
You can paint a room in 8 hours. Working together, you and your friend can paint the room in just 5. Let t be
the time (in hours) your friend would take to paint the room when working alone. Write and solve an equation to find
how long your friend would take to find how long your friend would take to paint the room when working alone.
 Hint: Work done  Work rate  Time
3.
7.5 PRACTICE:
In Exercises 1–3, solve the equation by cross multiplying. Check your solution(s).
3
1
4
6
3
x5



1.
2.
3.
x2
x2
x 1
x5
4x
x2
In Exercises 7–12, solve the equation by using the LCD. Check your solution(s).
4 2
5
1
9

 4


7.
8.
3
x
2x 4
2x
9.
x2
2x
3 
x3
x
In Exercises 10–15, solve the equation by using the LCD. Check your solution(s).
10.
4
1
x 1


x5 x
x5
11.
8
x8
3 
x
x4
12.
12
3
3


x  2x
x2
x
13.
x4
4x
5 
x5
x
14.
16
8
4


x  4x
x4
x
15.
x 1 1
2x  1


x2
x
x2
2
2
16. Determine whether the inverse is a function. Then, find the inverse:
𝑓(𝑥) =
2
𝑓(𝑥) =
𝑥−4
1
Other things to review for the quiz:
x 2  3x x 2  5 x  6
17.

x2
4x
19.
22.
12
3

5x 5x
14
6

x  7 x  18 x  9
2
20.
𝑓(𝑥) =
𝑥 2 +4
18.
11−2𝑥
x 2  5 x  14
  x 2  4 x  4
x3
7
3x

x2 x2
21.
15−
23.
4
2
𝑥
𝑥
+4
5
6
5x

x4 x3