Question

Question

John threw a rock into a lake from a bridge 124 feet above the river's surface. The rock sinks 81 feet below the river’s surface. What is the distance between the elevations? (Hint: Draw a picture or use a number line.)

Answer 1

To determine the distance between the elevations, we can set up a number line or visualize the scenario based on the given information.

1. Starting Point: The height of the bridge above the river's surface is 124 feet.
2. Sinking Depth: The rock sinks 81 feet below the river's surface.

To find the elevation of the rock relative to a reference point, we consider the elevations as follows:

• The elevation of the top of the bridge (where John throws the rock) is $+124\text{ feet}$.
• The elevation of the river's surface is $0\text{ feet}$.
• The elevation of the rock at its lowest point (81 feet below the river's surface) can be calculated as: $$0\text{ feet}-81\text{ feet}=-81\text{ feet}$$

Now, we need to find the distance between these two elevations:

• The top of the bridge is at $+124$ feet.
• The lowest point of the rock is at $-81$ feet.

To find the distance between these two points, we calculate: $$\text{Distance}=124-(-81)=124+81=205\text{ feet}$$

Thus, the distance between the elevations is $\boxed{{\displaystyle 205}}$ feet.