Help with this problem. How do you setup equation

Question

During the first part of a canoe trip, May paddled 20 km up stream and 20 km back in a total time of 5 hrs. The speed of the river is 3 km/hr. Find May's speed in still water. Set up the equation first then solve.

Answer 1

Dear Karen,

 

Question:  What is May's speed in still water? 

 

Let "X=speed in still water"

 

     .___20Km____> upstream      Note:  distance1=distance2          d=r*time   and   t=d/rate            

 

     <__20Km ____.  downstream            total time=5 hours     time upstream +  time downstream =total time

 

Now, make a table for all the above data:

 

 

d                =     r     *      t= d/r____________________

20 km            X+3            20 km/ X+3          upstream travel

 

20 km            X-3             20 km/ X-3          downstream travel

                                         5 hours                 total time

 

 

 

upstream time + downstream time = total time      Use substitution.

 

 

20/ (X+3)      +  20/(X-3)    = 5      You need a common factor to multiply each term by in order to get

 

 

rid of the fractions.    Multiply (X+3) by (x-3), and you got the common factors.  Use this for each term.

 

 

(X+3)(X-3)    20/(X+3)    +  20/ (X-3)     (X+3)(X-3)= 5 (X+3)(X-3)   Simplify by canceling like factors

 

             

               20(X-3)       +    20 (X+3)     =  5 (X² +3X -3X-9)=5(X²-9)

 

              20X-60 + 20X+60 = 5X² -45       The +60 and -60 cancel each other out.

                         

                             40X=5X²-45                    Simplify by writing equation in standard quadratic form.

                             0= 5X² +40X -45          Simplify by dividing every term by 5.

 

                             0= X² + 8X-9                  Factor, but use only a positive answer for X.

                      

                             0=(         )(        )

 

 

X=  _____km/1hour=speed of still water              Answer

 

 

If I have helped you, please give me a thumbs up. Also, if there are any questions on this problem, let me know.

                                                     Susan C.