Question
Nancie and Suresh are typing.
The rate at which Nancie is typing is represented by the equation y = 35x, where x is the time in minutes and y is the total number of words typed.
The rate at which Suresh is typing is represented by this table.
Select answers from the drop-down menus to correctly complete the statements.
Nancie types at a rate of
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words per minute and Suresh types at a rate of
Choose...
words per minute. Nancie's rate is
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Suresh's rate.
Time (min) Total words
0.5 28
3 168
14
784
The rate at which Nancie is typing is represented by the equation y = 35x, where x is the time in minutes and y is the total number of words typed.
The rate at which Suresh is typing is represented by this table.
Select answers from the drop-down menus to correctly complete the statements.
Nancie types at a rate of
Choose...
words per minute and Suresh types at a rate of
Choose...
words per minute. Nancie's rate is
Choose...
Suresh's rate.
Time (min) Total words
0.5 28
3 168
14
784
Answers
GPT-4o mini
To solve the question, we first need to establish the typing rates of both Nancie and Suresh.
### Nancie's Typing Rate
From the equation given for Nancie's typing rate, \(y = 35x\):
- Here, \(y\) represents total words typed and \(x\) is the time in minutes.
- The coefficient 35 indicates that Nancie types at a rate of **35 words per minute**.
### Suresh's Typing Rate
We can derive Suresh's rate from the data provided in the table:
1. **At 0.5 minutes**:
- Total words = 28
- Words per minute = \( \frac{28 \text{ words}}{0.5 \text{ minutes}} = 56 \text{ words per minute} \)
2. **At 3 minutes**:
- Total words = 168
- Words per minute = \( \frac{168 \text{ words}}{3 \text{ minutes}} = 56 \text{ words per minute} \)
3. **At 14 minutes**:
- We need to find the total words typed.
- Since the rate is consistent, we can use the previously found rate for Suresh:
- Total words = \( 56 \text{ words per minute} \times 14 \text{ minutes} = 784 \text{ words} \)
### Final Answers
Now we can fill in the answers:
- Nancie types at a rate of **35** words per minute and Suresh types at a rate of **56** words per minute. Nancie's rate is **less than** Suresh's rate.
So the completed statements are:
Nancie types at a rate of **35** words per minute and Suresh types at a rate of **56** words per minute. Nancie's rate is **less than** Suresh's rate.
### Nancie's Typing Rate
From the equation given for Nancie's typing rate, \(y = 35x\):
- Here, \(y\) represents total words typed and \(x\) is the time in minutes.
- The coefficient 35 indicates that Nancie types at a rate of **35 words per minute**.
### Suresh's Typing Rate
We can derive Suresh's rate from the data provided in the table:
1. **At 0.5 minutes**:
- Total words = 28
- Words per minute = \( \frac{28 \text{ words}}{0.5 \text{ minutes}} = 56 \text{ words per minute} \)
2. **At 3 minutes**:
- Total words = 168
- Words per minute = \( \frac{168 \text{ words}}{3 \text{ minutes}} = 56 \text{ words per minute} \)
3. **At 14 minutes**:
- We need to find the total words typed.
- Since the rate is consistent, we can use the previously found rate for Suresh:
- Total words = \( 56 \text{ words per minute} \times 14 \text{ minutes} = 784 \text{ words} \)
### Final Answers
Now we can fill in the answers:
- Nancie types at a rate of **35** words per minute and Suresh types at a rate of **56** words per minute. Nancie's rate is **less than** Suresh's rate.
So the completed statements are:
Nancie types at a rate of **35** words per minute and Suresh types at a rate of **56** words per minute. Nancie's rate is **less than** Suresh's rate.