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 an 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
A: y = 10x
B: y = 0.1x
C: y = 0.125x
D: 8x
To find the equation that represents the relationship between the number of miles (y) and the time in minutes (x) for the day you ran the fastest, we need to find the day with the lowest time and the corresponding number of miles ran.
On Monday, you ran 4 miles in 40 minutes, which means your speed was 4 miles/40 minutes = 0.1 miles per minute.
On Wednesday, you ran 2 miles in 16 minutes, which means your speed was 2 miles/16 minutes = 0.125 miles per minute.
Since Wednesday's speed (0.125 miles per minute) is greater than Monday's speed (0.1 miles per minute), Wednesday must be the day you ran the fastest.
Thus, the equation that represents the fastest day is:
y = 0.125x
Therefore, the correct answer is option C: y = 0.125x.
To find the equation that relates the number of miles (y) to the time in minutes (x) for the day you ran the fastest for the week, we need to determine the fastest pace achieved.
On Monday, you ran 4 miles in 40 minutes, which gives a pace of 40 minutes / 4 miles = 10 minutes per mile.
On Wednesday, you ran 2 miles in 16 minutes, which gives a pace of 16 minutes / 2 miles = 8 minutes per mile.
Comparing these two paces, we can see that running on Wednesday had the fastest pace. Therefore, the equation relating y and x for the day you ran the fastest is:
D: y = 8x
To determine the day you ran the fastest for the week, we need to compare the rates at which you ran on Monday and Wednesday. The rate is calculated by dividing the number of miles by the time taken.
On Monday, you ran 4 miles in 40 minutes, so the rate would be:
Rate on Monday = 4 miles / 40 minutes = 0.1 miles/minute
On Wednesday, you ran 2 miles in 16 minutes, so the rate would be:
Rate on Wednesday = 2 miles / 16 minutes = 0.125 miles/minute
Since the rates are different, we need to find the higher rate. The equation that represents the number of miles (y) as a function of time in minutes (x) would be the equation with the higher rate.
Comparing the rates, we can see that the rate on Wednesday (0.125 miles/minute) is higher than the rate on Monday (0.1 miles/minute).
Therefore, 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 is:
C: y = 0.125x