1. Ch 11: Rationals G) Work Word Problems
Objective:
To solve word problems involving people working together to complete a task.

2. I can paint a room in 4 hours
Demonstration
Jeff
Hal
That’s fast!
It takes me 5 hrs
I can paint a room in 4 hours
How long will it take to paint a room if we work together?

3. 1 room Work RateJeff = 4 hours Jeff 1 hr 1 hr 1 hr 1 hr
I can get ¼ of the room painted each hour that I work
I can paint a room in 4 hours
Jeff

4. 1 room Work RateHal = 5 hours Hal 1 hr 1 hr 1 hr 1 hr 1 hr
I can get ⅕ of the room painted each hour that I work
It takes me 5 hrs to paint a room
5 hours
Hal

5. Jeff Hal Work RateJeff + Work RateHal = Work RateTogether 5 + 4 per hr
I can get ⅕ of the room painted each hour that I work
I can get ¼ of the room painted each hour that I work
How long will it take to paint a room if we work together?
Work
RateJeff +
Work
RateHal =
Work
RateTogether
5 + 4
per hr
hrs + = = = 20

6. Use the table below to set up the equation.
Rules
Calculate the rate of work for each person.
Multiply the “work rate” by the total amount of “time” to determine the amount of “Work” each person contributes to the task.
Add the “Work” for each person and set that value equal to 1 task.
Use the table below to set up the equation.
Work Rate
Time
Work
Person 1 × = +
Person 2 × = =
1 task

7. Work Rate Time Work Done Jeff × = Hal × = 1 room + = 1 Example 1
Jeff can paint a room in 4 hours. It takes Hal 5 hours to paint the same room. How long will it take them if they work together?
Work Rate
Time
Work Done
Jeff × =
Hal × =
1 room + = 1

8. Work Rate Time Work Done Hose 1 × = Hose 2 × = 1 pool + = 1 Example 2
One water hose can fill a pool in 10 hours. A different hose only takes 6 hours. How long would it take if both hoses are used?
Work Rate
Time
Work Done
Hose 1 × =
Hose 2 × =
1 pool + = 1

9. Work Rate Time Work Done Hose 1 × 4 + x = Hose 2 × 4 = 1 cake + = 1
Example 3
Julie can complete a wedding cake in 8 hours. Marty can put one together in 10 hours. If Julie and Marty work together for 4 hours, how long will it take Julie to finish the job alone?
Work Rate
Time
Work Done
Hose 1 × 4
+ x =
Hose 2 × 4 =
1 cake + = 1

10. Work Rate Time Work Done Matt × 4.95 = Kim × 4.95 = 1 attic + = 1
Example 4
Working alone, Matt can clean an attic in 11 hours. One day his friend Kim helped him and it only took 4.95 hours. How long would it take Kim to do it alone?
Work Rate
Time
Work Done
Matt ×
4.95 =
Kim ×
4.95 =
1 attic + = 1

11. Classwork 1) Work Rate Time Work × = _______ × = _______
It takes Wilbur 9 hours to mop a warehouse. Bill can mop the same warehouse in 10 hours. How long will it take them if they work together?
Work Rate
Time
Work × =
_______ × =
_______

12. 2) Work Rate Time Work × = _______ × = _______
Working alone, Ryan can pick 40 bushels of apples in 10 hours. Darryl can pick the same amount in 15 hours. How long will it take them if they work together?
Work Rate
Time
Work × =
_______ × =
_______

13. 3) Work Rate Time Work × = _______ × = _______
It takes Ming 14 hours to tar a roof. Willie can tar the same roof in 8 hours. If they work together, how long will it take them?
Work Rate
Time
Work × =
_______ × =
_______

14. 4) Work Rate Time Work × = _______ × = _______
Working alone, Scott can dig a 10’ x 10’ hole in 8 hours. Mark can dig the same hole in 9 hours. How long will it take if they work together?
Work Rate
Time
Work × =
_______ × =
_______

15. 5) Work Rate Time Work × = _______ × = _______
Beth can oil the lanes in a bowling alley in 10 hours. One day her friend Shawna helped her and it only took 4.44 hours. How long would it take Shawna to do it alone?
Work Rate
Time
Work × =
_______ × =
_______

16. 6) Work Rate Time Work × = _______ × = _______
Joe can tile the kitchen floor in 7 hours. His wife decided to help him and they got the job done in 3.93 hours. How long would it have taken his wife to do it by herself?
Work Rate
Time
Work × =
_______ × =
_______