1. 7.8 Work Problems
Purpose: To solve word problems involving to job rates working together to get one job done.
Homework: Finish Worksheet and p #5-16 all.

2. Work Rates Teresa can paint a room in 4 hours.
Her work rate is ¼ because 1 job is done in 4 hours.
What is Beatrice’s work rate if it takes her 8 hours to wallpaper a room?
1/8

3. One printing press can finish a job in 8 h
One printing press can finish a job in 8 h. The same job would take a second press 12 h. How long would it take both presses together?
Work Rate 
 Time
Work Done 
1st
1/8   x
x/8 
2nd 
1/12  x 
 x/12
x + x = 1 (job done) ***LCD is 24.
24[x/8 + x/12] = 24(1) ; 3x + 2x = 24
5x = 24; x = 4 4/5 or 4.8 hours OR 4 hrs. 48 min

4. (n + 1/3) + 2/9 = 1 (job done) **LCD is 9 9[(n + 1/3) + 2/9] = 1(9)
An installer can carpet a room in 3 h. An assistant takes 4½ h to do the same job. If the assistant helps for 1 h and then leaves, how long will it take the installer?
Work Rate 
Time 
Work Done 
 Installer
1/3 
n + 1 
n + 1/3 
 Assistant
1÷9/2 = 2/9  1 
 2/9
(n + 1/3) + 2/9 = 1 (job done) **LCD is 9
9[(n + 1/3) + 2/9] = 1(9)
3(n + 1) + 2 = 9 ; 3n = 9 ; 3n + 5 = 9
3n = 4 ; n= 4/3 or 1 ⅓ h OR 1 hr 20 min for the installer to finish.

5. ¾ + 10/x = 1 (Job Done) **LCD is 4x 4x[3/4 +10/x] = 4x(1)
Jack can rake leaves in 40 min. He rakes for 20 min and is joined by Jill. If they rake the remaining leaves in 10 min, how long will it take Jill by herself?
Work Rate 
 Time
 Work Done
 Jack
 1/40
30 
 3/4
Jill 
1/x 
10 
 10/x
¾ + 10/x = 1 (Job Done) **LCD is 4x
4x[3/4 +10/x] = 4x(1)
3x +40 = 4x ; 40 = x
Jill’s work rate is 40 min.