Answers to Homework (12-8)
1) a = 4
3) c = 1
5) m = 1/3
7) p = -13/2
9) x = -4
11) z = -3, z = 2
13) e = 1
Warm ups
2 x  11y
y  3x

5 x  10 y 5 x  10 y
2
5 4


x  3 3x x
Work Problems
Objective: To solve work
problems involving rational
expressions (combined time).
Standard 5.0
Use this formula:
together together

1
alone1
alone2
Word Problem Notes 1
3) Working alone, Danielle can sweep a porch in
13 minutes. Gariella can sweep the same porch in
15 minutes. Find how long it would take them if
they worked together.
Word Problem Notes 1
4) It takes Kali 12 minutes to sweep a porch.
James can sweep the same porch in 13 minutes.
Find how long it would take them if they worked
together.
Word Problem Notes 1
5) It takes Daniel 15 hours to pick forty bushels of
apples. Shawna can pick the same amount in 11
hours. If they worked together, how long would it
take them?
Word Problem Notes 1
6) It takes Ryan 14 minutes to inflate twenty
balloons. Jessica can inflate the same twenty
balloons in 13 minutes. Find how long it would
take them to work together.
WATCH OUT!
A bathtub fills in 15 minutes when the drain is
closed. When the drain is open and the faucet is
off, the tub drains in 20 minutes. How long
would it take to fill the tub if the drain is open
and the faucet is on?
LCD: 60
3
4 60 x 60x

 1 60
15
20
4 x  3 x  60
x  60 min
TOO
• Anne can complete a project in 6 hours. It
takes Will 9 hours to do the same job. How
long will it take them if they work together?
•
•
•
•
18/5 hours
3 3/5 hours
3.6 hours
3 hours 36 minutes
Homework
• Worksheet:
▫ Problem Solving: Work Problems
Warm ups
2x
x
2
x + 8x + 7 x + 7
x
1
=1
3x +12 x + 4
Solving Review
4
1
= 1x+3
x-3
1 x+3
+
=1
5 10
Math Lab Review–
If it takes Joe 45 minutes to prepare 20 greeting
cards and it takes Lisa 30 minutes to prepare 20
greeting cards, how long will it take if they work
together?
Joe 1 job
45 min
Lisa 1 job
30 min
x = time in minutes to work together
together together

1
alone1
alone2
Equation
together together

1
alone1
alone2
LCD: 90
3
2 90 x 90x
45

30
 1 90
2 x  3 x  90
5 x  90
x  18 min
Math Lab 1
• Working alone, Franky can sweep a porch in 13
minutes. Brian can sweep the same porch in 15
minutes. Find how long it would take them if
they worked together?
Math Lab 2
• It takes Emma 12 minutes to eat Kyle’s candy.
Michelle can eat Kyle’s candy in 8 minutes.
How long would it take them if they worked
together?
Math Lab 3
• Working alone, H can wash her car in 3 hours.
Natalie can wash her car in 30 minutes. Find
how long it would take them if they worked
together.
Math Lab 4
• Working alone, Ava can plant a tree in 6 hours.
Maro can plant a tree in 5 hours. Find how long
it would take them if they worked together.
Practice Test Time!
• Multiple choice
• Show all of your work 
• Stay on task