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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