warm – up #5 1. annie and matt are 1200 miles apart when they started driving towards each other....
TRANSCRIPT
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