Question

A drowning swimmer is 28 feet from a point Q on a straight shoreline. The line from the swimmer to Q i perpendicular to the shoreline. If there is a lifeguard 82 feet from point Q along the shoreline, and the lifeguard can run 8 feet per second and swim 5 feet per second. How many feet from point Q should the lifeguard stop running along the shoreline and start swimming to get the the drowning swimmer fastest? The lifeguard should stop running and start swimming feet from point Q. Round to the nearest whole foot.

Answer 1

To find the point where the lifeguard should stop running and start swimming to reach the drowning swimmer fastest, we need to determine the time it takes for the lifeguard to reach the swimmer by running and swimming.

Step-by-step explanation:

To find the point where the lifeguard should stop running and start swimming to reach the drowning swimmer fastest, we need to determine the time it takes for the lifeguard to reach the swimmer by running and swimming.

Let the distance between the point Q and the lifeguard be x.

Using the distance formula, we can create two equations:

Equation 1: x^2 + 28^2 = 82^2

Equation 2: x/8 + (82-x)/5 = t

Solving these equations will give us the value of x, which represents the distance from point Q where the lifeguard should stop running and start swimming.