Let's call the speed of the river "r". The speed of the current in the downstream direction is 9 + r mph, and the speed of the current in the upstream direction is 9 - r mph. The time it takes to travel downstream and return upstream is the same, so we can set up the following equation:
(32 miles) / (9 + r mph) + (32 miles) / (9 - r mph) = 9 hours
We can simplify this equation by converting hours to minutes and miles to feet, and then simplify further by multiplying both sides of the equation by the denominators:
32 * 60 * (9 + r) + 32 * 60 * (9 - r) = 9 * 60 * (9 + r) * (9 - r)
Expanding the right side of the equation and simplifying:
32 * 60 * (9 + r) + 32 * 60 * (9 - r) = 810 * (9 + r) * (9 - r)
Expanding the left side of the equation and simplifying:
32 * 60 * 9 + 32 * 60 * r + 32 * 60 * 9 - 32 * 60 * r = 810 * (9 + r) * (9 - r)
Combining like terms and solving for r:
32 * 60 * 9 * 2 = 810 * (9 + r) * (9 - r)
96720 = 810 * (9 + r) * (9 - r)
Dividing both sides by 810:
119 = (9 + r) * (9 - r)
Expanding the right side of the equation:
119 = 81 - r^2
Adding r^2 to both sides of the equation:
119 + r^2 = 81
Subtracting 81 from both sides of the equation:
38 + r^2 = 0
Taking the square root of both sides of the equation:
r = ± sqrt(38)
Since r is the speed of the current, it must be a positive value, so we take the positive square root:
r = sqrt(38) mph
The speed of the river (current speed) is approximately 6.17 mph.