a boat takes 2 hours longer to go 45 miles up a river than to return. If
the boat's speed in still water is 12 mph, what is the rate of the current

Let x = the rate of the current.
Therefore the boat's rate going against the current is slowed down by x mph
or 12-x

Similarly the boat's rate returning with the current is sped u by x mph
or 12+x

Make this chart

              Distance |  Rate  |     Time
_______________________|________|_____________
Going       |          |        |                 
Returning   |          |        |            

Fill in the two rates, 12-x going and 12+x returning:


              Distance |  Rate  |     Time
_______________________|________|_____________
Going       |          |  12-x  |                 
Returning   |          |  12+x  |            


Fill in the distances, both of which are 45 miles


              Distance |  Rate  |     Time
_______________________|________|_____________
Going       |    45    |  12-x  |                 
Returning   |    45    |  12+x  |            

Now use TIME = DISTANCE/RATE to fill in the two times.


              Distance |  Rate  |     Time
_______________________|________|_____________
Going       |    45    |  12-x  |   45/(12-x)     
Returning   |    45    |  12+x  |   45/(12+x)

Now use the part that we haven't yet used to make the equation:

>>...a boat takes 2 hours longer to go 45 miles up a river than to return...<<

Therefore 

TIME GOING = TIME RETURNING + 2 HOURS

45/(12-x) = 45/(12+x) + 2

Can you solve that?

If not post again

Answers: x = 3 and x = -48

We discard the negative answer.  The rate of the current is 3 mph.

Edwin
AnlytcPhil@aol.com