Question

Please help me with this math problem :)
A boat is located 12 miles from a dock. The boat begins traveling toward the dock, and after 9 minutes, the boat is 9 miles from the dock.
PA: Find the speed per minute the boat is traveling at. (Show work)
PB: Write an equation with the distance the boat is located from the dock as a function of time. After how much time will the boat arrive at the dock? (Show your work)
PC: Describe the relationship between the boat is located from the dock and the time the boat has been traveling.

Answer 1

Part A
Because at 9 minutes, it is 9 miles away from the dock, and it starts 12 miles from the dock, it must have traveled 3 miles. Since it travels 3 miles in 9 minutes, it will travel 3/9 = 1/3 miles per minute.

Part B
Because per each minute, it is traveling 1/3 of a mile, to calculate the distance from the time, you must multiply, by 1/3, or divide by 3. Then, since we are finding it's distance from the dock, we must take 12 and subtract it from time/3. So f(t) = 12 - t/3, where t is the time in minutes.

To calculate how long until it reaches the dock, you set the function equal to the 0 miles the boat needs to be from the dock., so 12 - t/3 = 0, t/3 = 12, therefore t = 36 minutes.

Part C
The distance in miles will always be 12 minus 1/3 of the time in minutes, we can tell this because of the function we made in Part B. This is a linear function.