Question

A motorboat moves across a lake at a constant speed. When it begins, it is 64

krn from the shore. After 17 minutes, it is 30 km from the shore. Which
function describes the motorboat's distance from the shore?
A. y = 2x+64
B. y=-2x+64
C. y=-17x+64
D. y=-17x+30

Answer 1

The motorboat's distance from the shore as a function of time is described by the linear equation y = -2x + 64, where 'y' represents the distance from the shore in km and 'x' is the time in hours.

Step-by-step explanation:

The student asked which function describes the motorboat's distance from the shore. To solve this, we need to find the relationship between the distance traveled by the motorboat and the time elapsed. Initially, the boat is 64 km from the shore and after 17 minutes (which is 17/60 hours since we need to work in consistent units), it is 30 km from the shore.

To find the rate of change, we calculate the distance change per unit of time, which is (64 km - 30 km) / (17/60 hours) = 34 km / (17/60) hours = 120 km/hour. The negative sign indicates distance is decreasing over time.

Now we can establish a linear equation with the initial distance being the y-intercept and the rate of change being the slope (it's negative because the distance is decreasing). We will use 'x' to represent time in hours. The equation would be:

y = -2x + 64

Therefore, the correct answer is B. y = -2x + 64.