To determine which equation represents the relationship between miles (Y) and time in minutes (X) based on your running data, let's start by analyzing the data from your runs:
- Monday's run: 4 miles in 40 minutes
- Wednesday's run: 2 miles in 16 minutes
Now, we can calculate the rates (miles per minute) for both days:
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Monday's rate: \[ \text{Rate} = \frac{4 \text{ miles}}{40 \text{ minutes}} = 0.1 \text{ miles per minute} \]
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Wednesday's rate: \[ \text{Rate} = \frac{2 \text{ miles}}{16 \text{ minutes}} = 0.125 \text{ miles per minute} \]
Next, we can express the relationship between miles (Y) and time in minutes (X) in the form of an equation.
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For Monday (where you run 4 miles in 40 minutes), the equation can be written as: \[ Y = 0.1X \]
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For Wednesday (where you run 2 miles in 16 minutes), the equation can be written as: \[ Y = 0.125X \]
Since the problem mentions finding an equation for the fastest run of the week, you should choose the run with the highest rate of miles per minute. The fastest rate is from Wednesday at 0.125 miles per minute.
Therefore, the correct equation to represent the fastest run is: \[ Y = 0.125X \]
The appropriate answer from the options given is (d) Y = 0.125X.