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We will be solving problems in Real Life by using the methods learned in week 4 for solving systems of equations

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We will be solving problems in Real Life by using the methods learned in week 4 for solving systems of equations.  Most everyone has a fear of word problems because you haven't had much experience in solving them.  If you just take them one step at a time, you will find them manageable and build your confidence in your ability to successfully tackle any word problem you meet. 

Remember:  I am here to help you!

Please read the prompt above to see additional instructions for your Initial Post.

Here is an example to get us started.  I am working out the entire problem for you, but in your initial post you only need to set up the situation and leave solving the problem to a classmate (see prompt given above).

APPLICATION PROBLEM:       DISTANCE = RATE X TIME A boat's crew rowed 12 miles downstream, with the current, in 1.5 hours.  The return trip, against the current, covered the same distance but took 4 hours.  Find the crews rowing rate in still water and the rate of the current.

The relationship we need to use is Distance = Rate x Time.  We will have two equations: one for the trip downstream and one for the trip upstream.  We have two variables: crews rowing rate in still water and rate of the current.

Let w = crews rowing rate in still water

Let c = rate of the current

Downstream: Distance = Rate x Time    Rate will be w+c (rate in still water + current)

         (1)                     12     = (w+c) 1.5 = 1.5w+1.5c

Upstream: Distance = Rate x Time    Rate will be w-c (rate in still water - current)

          (2)                    12      = (w-c) 4 = 4w-4c

One approach is to simplify the equations before solving the system. 

 (1)     12=1.5w+1.5c divide both sides by 1.5

           8 = w + c

(2)     12 = 4w=4c   divide both sides by 4

         3 = w - c

Use Elimination on the two equations           8 = w+c
          3 = w-c      After adding the two equations we have          11 = 2w     divide by 2

         w = 11/2 = 5.5 Use this value to solve for c. 

w+c = 8  

         5.5+c = 8

         c = 8 - 5.5

         c=2.5  

Therefore, the rate of the current is 2.5 and the rate of the crew rowing in still water is 5.5. I can't wait to see your posts.  You may use a scholarly resource, just remember to cite it.