Question
A diver descended 20 feet in 5 seconds. What is the average rate per second that he traveled? Explain how you can use integer tiles to solve the problem and find the answer.
Answers
GPT-4o mini
To find the average rate at which the diver traveled, we can start by calculating the rate per second that he descended.
The diver descended a total of 20 feet over a time span of 5 seconds. To find the average rate, we can use the formula for average speed:
\[
\text{Average Rate} = \frac{\text{Total Distance}}{\text{Total Time}}
\]
Substituting the values into the formula:
\[
\text{Average Rate} = \frac{20 \text{ feet}}{5 \text{ seconds}} = 4 \text{ feet/second}
\]
So the average rate at which the diver traveled is 4 feet per second.
### Using Integer Tiles to Understand the Problem
To visualize the problem using integer tiles:
1. **Representation of Distance and Time**: You could use tiles to represent the distance and time. Let's say each tile represents 1 foot of descent.
2. **Creating Groups**: You can create a strip of 20 tiles to represent the total distance of 20 feet. Then, you can think of dividing these tiles into 5 equal groups to represent the time of 5 seconds. Each group will represent the distance traveled in each second.
3. **Group Distribution**: If you take the 20 tiles (feet) and evenly distribute them into 5 groups (seconds), you would put 4 tiles (feet) into each group. This shows that for each of the 5 seconds, the diver travels 4 feet.
Using this method of integer tiles provides a visual representation of how the distance is divided over time, confirming that the average rate of descent is indeed 4 feet per second.
The diver descended a total of 20 feet over a time span of 5 seconds. To find the average rate, we can use the formula for average speed:
\[
\text{Average Rate} = \frac{\text{Total Distance}}{\text{Total Time}}
\]
Substituting the values into the formula:
\[
\text{Average Rate} = \frac{20 \text{ feet}}{5 \text{ seconds}} = 4 \text{ feet/second}
\]
So the average rate at which the diver traveled is 4 feet per second.
### Using Integer Tiles to Understand the Problem
To visualize the problem using integer tiles:
1. **Representation of Distance and Time**: You could use tiles to represent the distance and time. Let's say each tile represents 1 foot of descent.
2. **Creating Groups**: You can create a strip of 20 tiles to represent the total distance of 20 feet. Then, you can think of dividing these tiles into 5 equal groups to represent the time of 5 seconds. Each group will represent the distance traveled in each second.
3. **Group Distribution**: If you take the 20 tiles (feet) and evenly distribute them into 5 groups (seconds), you would put 4 tiles (feet) into each group. This shows that for each of the 5 seconds, the diver travels 4 feet.
Using this method of integer tiles provides a visual representation of how the distance is divided over time, confirming that the average rate of descent is indeed 4 feet per second.