Julie and eric row their boat at a constant speed of 48 miles downstream for 6 hours, by the current. rowing at the same rate, the trip back against the current takes 8 hours. find the rate of the current

Solve for the two velocities:
with the current = 48/6 = 8 mph
against the current = 48/8 = 6 mph
bv= boat velocity in still water
cv = current velocity
A) bv -cv = 6mph
B) bv + cv = 8mph
Adding both equations
2 * bv = 14 mph
boat velocity = 7 mph
current velocity = 1 mph
Calculator and tutorial can be found here:
http://www.1728.org/veloccal.htm

A. The shorter length will be neither of them since they have the same degrees.

B. The hypotenuses will be