# Objective - To solve chart problems involving work by 68fxOejs

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```									Objective - To solve chart problems
involving work.
Work Rate      Time  Work Done

Work Rate  Time  Work Done
1 Job
5 hrs. 1 Job
5 hrs.
or   1 Job/hr.
5
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     1                         1x
4            x            4
Hal      1                         1x
5            x            5
1 x  1x 1                  1
4     5
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     1                          1x
4               x          4
Hal      1                          1x
5               x          5

                
1x  1x 1                      1
20
4     5
5x  4x  20
x 20  2 2 hrs.
9x  20              9      9
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
10 hr.      1                       1 x
hose       10           x          10
6 hr.      1                       1x
x
hose       6                       6
1
1 x  1x 1
10     6
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
10 hr.      1                         1 x
hose       10              x         10
6 hr.      1                         1x
x
hose       6                         6

                 
1
30  1 x  1x 1
10     6
3x  5x  30              30  3 3 hrs.
x
8x  30              8      4
John can tile a 10’ x 10’ room in 80 minutes.
It takes Sam 2 hours. If John works alone for
30 minutes and then Sam helps him finish, how
much longer will the job take?
Work Rate    Time  Work Done
x  30 80       
1               1 x  30
John
80
Sam
1                    1 x
120         x       120
1
      120 x  1
1 x  30 
80
1
John can tile a 10’ x 10’ room in 80 minutes.
It takes Sam 2 hours. If John works alone for
30 minutes and then Sam helps him finish, how
much longer will the job take?
Work Rate     Time  Work Done
x  30 80       
1                1 x  30
John
80
Sam
1                    1 x
120         x       120

                       
1
240    
1 x  30 
80
 120 x  1
1

3 x  30  2x  240     x  30 min.
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
Julie     1
8           4x    8

1 4x

1                      4
Marty                   4
10                     10
1
    10
1 4 x  4 1
8
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
Julie     1
8           4x    8

1 4x

1                      4
Marty                   4
10                     10

                      
1
40      10
1 4 x  4 1
8
x 4 hr.
5(4  x)  16  40              48 min.
5
Two planes leave Chicago at the same time. The
westbound plane travels 900 miles. The eastbound
plane goes 150 mph faster and travels 1200 miles.
Find their speeds.
Rate  Time  Distance
West       r 450       t       900       rt d
r    r
East         600                               d
r + 150       t       1200         t
r
West           East
t 900           1200        900(r  150)  1200r
t
r           r  150    900r  135000  1200r
900  1200                 135000  300r
r    r  150                  450  r
Ann leaves school and walks home for 3.75 miles.
Mark runs home 1.5 mph faster than Ann. If he
lives 6 miles from home and they both leave and
arrive at the same time, how long did it take them?
Rate  Time  Distance
Ann       r 2.5       t 1.5     3.75     2.5t  3.75
2.5     2.5
Mark r + 1.5          t          6          t  1.5
Ann           Mark
t 3.75            6           3.75(r  1.5)  6r
t
r          r  1.5       3.75r  5.625  6r
3.75  6                        5.625  2.25r
r   r  1.5                      2.5  r
x4
The reciprocal of 4 less than x is three times the
reciprocal of x.
1           1
 3            Restrictions:
x4           x
x  4, x  0
1  3
x4 x
x  3(x  4)
x  3x  12
3x  3x
2x  12
2  2
x6

```
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