You are training twice a week for a race. On Monday, you go 4 miles in 40 minutes. Then on Wednesday you go 2 miles in 16 minutes. Write and equation where y is the number of miles and x is the time in minutes for the day you ran the fastest for the week.
Options:
Y = 8x
Y = 0.1x
Y = 0.125x
Y = 10x
Based on the given information, the equation representing the relationship between the number of miles (y) and the time in minutes (x) for the day you ran the fastest for the week would be:
Y = 0.125x
In order to find the equation where y is the number of miles and x is the time in minutes for the day you ran the fastest for the week, we need to compare the two running sessions and determine which one was the fastest.
On Monday, you ran 4 miles in 40 minutes, which means your pace was 4 miles / 40 minutes = 0.1 miles per minute.
On Wednesday, you ran 2 miles in 16 minutes, which means your pace was 2 miles / 16 minutes = 0.125 miles per minute.
Since 0.125 miles per minute is a faster pace than 0.1 miles per minute, the equation where y is the number of miles and x is the time in minutes for the day you ran the fastest is:
Y = 0.125x
Therefore, the correct option is Y = 0.125x.
To determine the equation representing the relationship between the number of miles (y) and the time in minutes (x) for the day when you ran the fastest during the week, we need to calculate the average speed for each workout.
On Monday, you ran 4 miles in 40 minutes. Therefore, your average speed was 4 miles / 40 minutes = 0.1 miles per minute.
On Wednesday, you ran 2 miles in 16 minutes. Thus, your average speed was 2 miles / 16 minutes = 0.125 miles per minute.
Since we are looking for the equation for the day when you ran the fastest, we need to choose the option with the larger coefficient in front of the x variable.
Comparing the coefficients:
- Option 1: Y = 8x (coefficient = 8)
- Option 2: Y = 0.1x (coefficient = 0.1)
- Option 3: Y = 0.125x (coefficient = 0.125)
- Option 4: Y = 10x (coefficient = 10)
The option with the larger coefficient is Y = 10x. Therefore, the correct equation is Y = 10x, where y represents the number of miles and x represents the time in minutes for the day when you ran the fastest during the week.