Question

Micah rows his boat on a river 4.48 miles downstream, with the current , 0.32 hours. He rows back upstream the same distance, against the current , 0.56 hours . Assuming his rowing speed of the cure are constant, what is the spend of the current

Answer 1

Short Answer: Current speed  =  3 miles per hour.
Givens
Downstream 
d = 4.48 miles
t  = 0.32 hours.
c = ??
r_boat = ??


Upstream
d = 4.48 miles
t = 0.56 miles
c = ??
r_boat =??

Equations. 
Since the distances are the same, you can equate the distances and come back to them later.
d = r*t
(r - c) * 0.56 = (r + c) * 0.32  This will give you r in terms of c. Notice the minus sign on the left. It's there because the current is going against you, slowing you down.  
Remove brackets
0.56r - 0.56c = 0.32r + 0.32c   Add 0.56c to both sides.
0.56r = 0.32r + 0.32c + 0.56c
0.56r = 0.32r + 0.88c               Subtract 0.32r from both sides.
0.56r - 0.32r = 0.88c
0.24r = 88c                               Divide by 0.24  
r = 0.88/0.24 c
r = 3 2/3 c

Now we have enough information to solve for c

4.48/(r + c) = 0.32
4.48 = 0.32 * (r + c)           Substitute r = 3 2/3c into this equation.
4.48 = 0.32 * (3 2/3c + c)   Add c and 3 2/3c together. 
4.48 = 0.32 * (4 2/3c)        Change 4 2/3 to  14/3
4.48 = 0.32 * 14/3 c 
4.48 = (4.48 / 3 ) * c
4.48 = 1.493333333 c      Divide 4.48 by 1.493333333
c = 4.48 / 1.4933333
c = 3 mph <<<<<<<<<<<<<<Answer