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 \( \boxed{205} \) feet.