Explanation:
Rate upstream = b -w b = boat speed w = water speed
Rate downstream = b+w distance is given as 22 miles
distance / rate = time
22/ (b-w) + 22 / ( b+w) = 6.5 multiply the entire equation by (b+w)(b-w) :
22(b+w) + 22 (b-w) = 6.5 ( b+w)(b-w)
44b = 6.5 b^2 - 6.5w^2 re-arrange
6.5 w^2 = 6.5 b^2 - 44b we know b = 13 (given) solve for w
6.5 w^2 = 526.5
w = 9 m/hr