32) A motorboat traveling with the current can go 24 miles in 2 hrs. Against the current, it takes 3 hrs to go the same distance. Find the rate of the motorboat in calm water.*1 pointA) 2 miles per hrB) 4 miles per hrC) 8 miles per hrD) 10 miles per hr

To solve this problem, we need to understand that the speed of the boat in calm water plus the speed of the current equals the speed of the boat with the current. Conversely, the speed of the boat in calm water minus the speed of the current equals the speed of the boat against the current.

Step 1: Let's denote the speed of the boat in calm water as 'b' and the speed of the current as 'c'.

Step 2: From the problem, we know that the boat travels 24 miles in 2 hours with the current. So, the speed of the boat with the current is 24 miles / 2 hours = 12 miles per hour. This gives us the equation b + c = 12.

Step 3: We also know that the boat travels 24 miles in 3 hours against the current. So, the speed of the boat against the current is 24 miles / 3 hours = 8 miles per hour. This gives us the equation b - c = 8.

Step 4: Now we have a system of two equations, and we can solve it. If we add these two equations together, we get 2b = 20, so b = 10 miles per hour.

So, the speed of the motorboat in calm water is 10 miles per hour. The correct answer is D) 10 miles per hour.