ohn 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.)

Question

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(1 point)
Responses

-205 feet
-205 feet

43 feet
43 feet

-43 feet
-43 feet

205 feet

Answer 1

To find the distance between the elevations of the bridge and the lowest point the rock reaches after sinking in the lake, we can consider the following:

1. The height of the bridge above the river's surface is 124 feet. Let's represent this point as \( 124 \).
2. The rock sinks 81 feet below the river's surface. So, the elevation of the rock below the river surface can be calculated as: \[ 0 - 81 = -81 \text{ feet} \] where 0 represents the elevation of the water's surface.

Now we need to find the difference between the height of the bridge and the lowest point of the rock. We can calculate this as: \[ \text{Distance} = \text{Height of the bridge} - \text{Depth of the rock} \] \[ \text{Distance} = 124 - (-81) \] Since subtracting a negative number is the same as adding, we can rewrite this as: \[ \text{Distance} = 124 + 81 = 205 \text{ feet} \]

Therefore, the distance between the elevations is 205 feet.

Answer 2

are you sure

Answer 3

Let's go through the problem step by step to ensure we're calculating correctly.

1. The height of the bridge above the river's surface is 124 feet.
2. The rock sinks 81 feet below the river’s surface.

To find the total depth of the rock below the ground level (which is the bridge level of 124 feet), we can calculate its position as follows:

• The river's surface is at 0 feet (base level).
• The bottom of the lake where the rock sinks is: \[ 0 - 81 = -81 \text{ feet} \]

So, the elevation of the lake's surface is 0 feet, and the rock is at -81 feet relative to that surface.

Now, the distance between the bridge and the lowest point of the rock is: \[ \text{Distance} = \text{Height of the bridge} - \text{Depth of the rock} \] Putting in the values: \[ \text{Distance} = 124 - (-81) \] This simplifies to: \[ \text{Distance} = 124 + 81 = 205 \text{ feet} \]

So, the calculation confirms that the distance between the elevations is indeed 205 feet.

If you have an alternate interpretation or further information regarding the setup of the problem, please share, and we can reevaluate it!