Question
Write an equation to represent how many plates Ana has left to wash at a particular time after her start at 7:15. Explain your reasoning.
Answers
GPT-4o mini
To create an equation representing how many plates Ana has left to wash at a specific time after she started washing at 7:15, we need to consider a few variables:
1. Let \( P \) represent the total number of plates Ana starts with.
2. Let \( t \) represent the time in minutes that has elapsed since 7:15.
3. Let \( r \) represent the rate (in plates per minute) at which Ana washes the plates.
Now, the number of plates Ana has left to wash at time \( t \) can be calculated as the initial number of plates minus the number of plates she has washed in that time.
The equation can be written as:
\[
\text{Plates left} = P - rt
\]
### Explanation:
- **\( P \)**: This is the initial count of plates Ana needs to wash. For example, if she starts with 50 plates, \( P \) would be 50.
- **\( rt \)**: This term calculates how many plates Ana has washed by multiplying the time elapsed (\( t \)) by her washing rate (\( r \)). For example, if she washes 2 plates per minute, and \( t \) is 10 minutes, then she has washed \( 2 \times 10 = 20 \) plates.
- **Plates left**: This final expression gives the number of plates still needing to be washed at any time \( t \).
This equation assumes that Ana is consistently washing plates at a constant rate \( r \) throughout the period considered. Additionally, time \( t \) should not exceed the total time Ana spends washing plates, or the number of plates left would become negative, which implies she has finished washing.
1. Let \( P \) represent the total number of plates Ana starts with.
2. Let \( t \) represent the time in minutes that has elapsed since 7:15.
3. Let \( r \) represent the rate (in plates per minute) at which Ana washes the plates.
Now, the number of plates Ana has left to wash at time \( t \) can be calculated as the initial number of plates minus the number of plates she has washed in that time.
The equation can be written as:
\[
\text{Plates left} = P - rt
\]
### Explanation:
- **\( P \)**: This is the initial count of plates Ana needs to wash. For example, if she starts with 50 plates, \( P \) would be 50.
- **\( rt \)**: This term calculates how many plates Ana has washed by multiplying the time elapsed (\( t \)) by her washing rate (\( r \)). For example, if she washes 2 plates per minute, and \( t \) is 10 minutes, then she has washed \( 2 \times 10 = 20 \) plates.
- **Plates left**: This final expression gives the number of plates still needing to be washed at any time \( t \).
This equation assumes that Ana is consistently washing plates at a constant rate \( r \) throughout the period considered. Additionally, time \( t \) should not exceed the total time Ana spends washing plates, or the number of plates left would become negative, which implies she has finished washing.