Let

d = 33 mi the distance

c = 12 mph the speed of the current

t1 = the time of the trip with the current

t2 = the time of the trip against the current

t1 + t2 = 33 hr 40 min

33 hr 40 min = 33 2/3 hr

t1 + t2 = 33 2/3

t1 + t2 = 101/3

v = the average speed of the boat relative to the water

Since speed = distance/time follows time = distance/speed.

The speed of the boat when traveling with the current is: 'v + c' and the time is:

t1 = d/(v + c)

The speed of the boat when traveling against the current is: 'v - c' an the time is:

t2 = d/(v - c)

Now we can write:

t1 + t2 = 101/3

d/(v + c) + d/(v - c) = 101/3

33/(v + 12) + 33/(v - 12) = 101/3

........

click here to see the equation solved for v

........

v = 13 mph

The speed of the boat relative to the water is approximately 13 mph.