SOLUTION: I need help setting up this problem so I can solve it. Can anyone please help? A motor boat can run 25 mph in still water. The boat starts at 7:00 am going upstream in a river

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Question 74234: I need help setting up this problem so I can solve it. Can anyone please help?
A motor boat can run 25 mph in still water. The boat starts at 7:00 am going upstream in a river whose current runs at 5 mph. How far up the river can the boat go and still be back at 12:00 noon?
Thank You!
Found 2 solutions by checkley75, rmromero:
Answer by checkley75(3666)   (Show Source): You can put this solution on YOUR website!
DISTANCE=RATE*TIME. THE TWO DISTANCES ARE THE SAME THUS WE HAVE:
20X=30(5-X)
20X=150-30X
20X=30X=150
50X=150
X=150/50
X=3 HOURS GOING UP STEAM. THUS 2 HOURS(5-3=2) RETURN DOWN STREAM.
PROOF
20*3=30(5-3)
60=30*2
60=60
Answer by rmromero(383)   (Show Source): You can put this solution on YOUR website!


A motor boat can run 25 mph in still water. The boat starts at 7:00 am going upstream in a river whose current runs at 5 mph. How far up the river can the boat go and still be back at 12:00 noon? 





What is asked in the problem?

    How far up the river can the boat go and still be back at 12:00noon?



Given:

Rate of motor boat in still water is 25mph

Rate of the current is 5mph

Time ranges from 7:00am to 12:00noon. That's is 5 hours difference.



Representation:

Let x be the distance the boat travel up or down

    y = the time it takes the boat to travel upstream

  5 - y = the time it takes the boat to travel downstream





                rate     *      time          =       distance

Upstream       25 - 5             y           =         x



Downstream     25 + 5           5 - y         =         x





                      (25 - 5)y = x      eq1

                  (25 + 5)(5-y) = x      eq2



Solve using substitution method



                   20y = x

                30( 5 - y) = x

                150 - 30y = 20y

                 150 = 50y

                   3h = y  this is the time it takes the boat to 

                           travel upstream



               5 - y = 5 - 3

                     = 2 hours --> this is the time it takes the boat to 

                                   travel downstream

   when y = 3



               20y = x

               20(3) = x

                 60m = x  This is the distance travel either upstream 

                          or downstream





                

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