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

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?

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

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

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

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

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

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

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

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

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 × = _______ × = _______

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 × = _______ × = _______

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 × = _______ × = _______

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 × = _______ × = _______

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 × = _______ × = _______

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 × = _______ × = _______