Ch 11: Rationals G) Work Word Problems

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

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

1 hr 1 hr 1 hr 1 hr 1 hr 1 room Work RateHal = 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 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 hrs per hr = = + = 20

Rules Time Work Work Rate Person 1 × = + Person 2 × = = • 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. 1 task

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? Time Work Done Work Rate Jeff × = = Hal × 1 room + = 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? Time Work Done Work Rate Hose 1 × = = Hose 2 × 1 pool + = 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? Time Work Done Work Rate Hose 1 × 4 + x = = Hose 2 × 4 1 cake + = 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? Time Work Done Work Rate Matt × 4.95 = = Kim × 4.95 1 attic + = 1

Classwork 1) 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? Time Work Work Rate × = _______ × = _______

2) 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? Time Work Work Rate × = _______ × = _______

3) 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? Time Work Work Rate × = _______ × = _______

4) 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? Time Work Work Rate × = _______ × = _______

5) 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? Time Work Work Rate × = _______ × = _______

6) 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? Time Work Work Rate × = _______ × = _______

Ch 11: Rationals G) Work Word Problems