Marissa can travel 12 miles upstream or 16 miles upstream or 16 miles downstream in the same amount of time What is the speed of her motorboat in still water?

Question

please help this is for algebra 2.

 

Answer 1

 

Let t = time for each direction of the trip (time is same for both upstream and downstream)

Let w = rate of the water current

Let b = rate of boat in still water

 

UPSTREAM:   (subtract the water current rate from the boat rate)

 

     Rate • Time = Distance

     (b - w)t = 12

 

DOWNSTREAM:   (add the water current to the boat rate)

 

     Rate • Time = Distance

     (b + w)t = 16

 

Simplifying the above equations,

 

    (EQ 1)     tb  - wt = 12

    (EQ 2)     tb + wt = 16

 

Adding the equations together, and dividing by 2 gives us

 

    2tb = 28

     tb = 14

 

    (EQ 3)    tb = 14

 

Since tb = 14 we can take and substitute in that value

 

    tb - wt = 12   

    14 - wt = 12

           wt = 2

 

That gives us the following system of equations

 

     wt = 2

     tb = 14

 

Dividing both sides off both equations by t gives us

 

     w = 2/t

     b = 14/t

 

Taking equation 3 from several steps above,

 

    (EQ 3)    tb = 14

 

Substitute 14/t for b

 

     tb = 14

     t(14/t) = 14

    14 = b

 

The boat's speed is 14 miles per hour