Warm – up #51. Annie and Matt are 1200 miles apart when they started driving towards each other. Annie is driving at 70 mph, and Matt is driving at 80 mph. When will they pass each other? Rate Time Distance

Annie

Matt

Total

x

80

70

x

70x

80x

70x + 80x = 1200

• =1200

8 hrs

Homework LogThurs

10/8

Lesson 2 – 2

Learning Objective: To solve work problems

Hw: #206 Pg. 113 #33 – 38 all& RE-DO 4, 11, 15, 26, 29

10/8/15 Lesson 2 – 2 Work Problems Day 4

Advanced Math/Trig

Learning Objective

To solve work problems

WorkIf it takes 6 hours to complete 1 job, what part of the job is complete in 1

hour?

If it takes 4 hours to complete 1 job, what is the rate?

1Rate

6

1

4

Work Problem1. James can dig a ditch in 5 days and Toby can dig a ditch in 2 days. How long will it take for both James & Toby to dig the ditch if they work together?

AloneRate

Time Together

Part of Job

Completed

James

Toby

x

x

James’s part + Toby’s part = 1 Whole Job Completed

• =1

51

2

5

x

2

x

AloneRate

Time Together

Part of Job

Completed

James

Toby

x

x

James’s part + Toby’s part = 1 Whole Job Completed

• =1

51

2

5

x

2

x

15 22 5 10

7 10

x x

x x

x

10 31 days 1 day 10 hours

7 7x

(10) (10)(10)

Work Problem #1 Cont’d

Drain/Work Problem2. An Olympic sized pool can be filled by pipe A in 18 hours and by pipe B in 12 hours.  There is also a drain pipe that drains the entire pool in 8 hours.  If the valves of pipe A, pipe B and the drain pipe are open, how long will it take to fill the pool?

AloneRate

Time Together

Part of Job

Completed

Pipe A

Pipe B

Drain Pipe

x

x

• =1

181

12

18

x

12

x

1

8 x

8

x

AloneRate

Time Together

Part of Job

Completed

Pipe A

Pipe B

Drain Pipe

x

x

• =1

181

12

18

x

12

x

1

8 x

8

x

Pipe A’s part + Pipe B’s part + Drain’s part= 1 Whole Job Completed

118 12 84 6 9 72

x x x

x x x

72x

(72) (72) (72)(72)

hours

Drain/Work Problem #1 Cont’d

Work Problem3. Working together, Karlie and Erin can sweep a porch in 5.65 minutes. If Erin worked alone, it would have taken her 10 minutes. How long does it take Karlie to sweep the porch alone?Alone

RateTime

TogetherPart of

JobComplete

d

Karlie

Erin

5.65

5.65

Karlie’s part + Erin’s part = 1 Whole Job Completed

• =𝟏𝟏𝟎

𝟏𝒙

𝟓 .𝟔𝟓𝒙

𝟓 .𝟔𝟓𝟏𝟎

AloneRate

Time Together

Part of Job

Completed

Karlie

Erin

5.65

5.65

Karlie’s part + Erin’s part = 1 Whole Job Completed

• =Work Problem #3

Cont’d

𝟏𝟏𝟎

𝟏𝒙

𝟓 .𝟔𝟓𝒙

𝟓 .𝟔𝟓𝟏𝟎

5.65𝑥

+5.6510

=1(1 0 𝑥) (1 0 𝑥)(1 0 𝑥)

56.5 + 5.65x = 10x56.5 = 4.35x

12.99 minutes

Work Problem4. A tank can normally be filled in 6 hours. But after the tank developed a leak, it took 10 hours to fill. How long would it take the leak to empty the full tank? Alone

RateTime

TogetherPart of

JobComplete

d

Fill

Leak

10

10

Fill + Leak = 1 Tank Emptied

• =−𝟏𝒙

𝟏𝟔

𝟏𝟎𝟔

−𝟏𝟎𝒙

AloneRate

Time Together

Part of Job

Completed

Fill

Leak

10

10

Fill + Leak = 1 Tank Emptied

• =Work Problem #4

Cont’d

−𝟏𝒙

𝟏𝟔

𝟏𝟎𝟔

−𝟏𝟎𝒙

106

+−10𝑥

=1(6 𝑥) (6 𝑥)(6 𝑥)

10x – 60 = 6x4x = 60

15 hours

Work Problem5. It takes Sam and Sabrina 20 hours to build a Lego set, and Sabrina works four times as fast as Sam. How long would it take if Sam worked alone?

AloneRate

Time Together

Part of Job

Completed

Sabrina

Sam

20

20

Sam’s Part + Sabrina’s Part = 1 Job Completed

• =𝟏𝟒𝒙

𝟏𝒙

𝟐𝟎𝒙𝟐𝟎𝟒𝒙

AloneRate

Time Together

Part of Job

Completed

Sabrina

Sam

20

20

Sam’s Part + Sabrina’s Part = 1 Job Completed

• =Work Problem #5

Cont’d

𝟏𝟒𝒙

𝟏𝒙

𝟐𝟎𝒙𝟐𝟎𝟒𝒙

20𝑥

+204 𝑥

=1(4 𝑥) (4 𝑥)(4 𝑥)

80 + 20 = 4x100 = 4x

100 hoursx = 25

Ticket Out the Door

Cody can harvest a field in 11 hours. One day, his friend Luke helped him and it only took 5.96 hours. How long would it take Luke to do it alone?

Homework

#206 Pg. 113 #33 – 38 all

& RE-DO 4, 11, 15, 26, 29