Let r be the speed of the current. Going upstream the boat goes at speed 30-r, going downstream at 30+r. If we're going 36 miles each way, the total time 2.5 hours is
2.5 = 36 / (30-r) + 36/(30+r)
[tex]\dfrac{2.5}{36} = \dfrac{30 + r + 30 - r}{(30 + r)(30 - r)}[/tex]
(25/360)(900-r²) = 60
900 - r² = 60(360)/25
r^2 = 900 - 60(360)/25 = 36
We choose the positive square root from the way we set up the problem.
r = 6
Answer: 6 miles per hour
