SOLUTION: a canoeist travels 4 miles downstream in 1 hour. the return trip takes 1.5 hours.Write the equations to solve the problem. what's the rate of the boat in still water

Let c be the rate of the current; r is the rate for the boat if no current.
The use of the subscripts are d for DOWNSTREAM and u for UPSTREAM.

             speed       time       distance
TO           r+c                d
FROM         r-c                d


Note that the unknown variables in the problem description are r and c.

Let speed of boat, in still water be S, and speed of current, C

Total speed downstream is: S + C

Total speed upstream is: S – C

The downstream speed equation is thus formed: ___S + C = 4___C = 4 - S ---- eq (i)

The upstream speed equation is also formed: , or 1.5S - 1.5C = 4 -------- eq (ii)

1.5S - 1.5(4 – S) = 4 ---------- Substituting 4 – S for C in eq (ii)

1.5S - 6 + 1.5S = 4

1.5S + 1.5S = 4 + 6

3S = 10

S, or speed of boat in still water = , or  mph