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.
Let's assume that the fastest day you ran during the week is on Monday.
The equation would be:
y = 4 - (x/10)
Where:
- x represents the time in minutes (since 40 minutes = 4 miles, we divide x by 10 to keep the same ratio)
- y represents the number of miles you ran on that day
Please note that this equation assumes a linear relationship between time and distance for your running speed.
To determine the day you ran the fastest for the week in terms of the number of miles and time in minutes, we need to calculate the average speed (miles per minute) for each day.
Average Speed = Total Distance / Total Time
For Monday:
Distance = 4 miles
Time = 40 minutes
Average Speed1 = 4 miles / 40 minutes = 0.1 miles/minute
For Wednesday:
Distance = 2 miles
Time = 16 minutes
Average Speed2 = 2 miles / 16 minutes = 0.125 miles/minute
Since we want to find the day you ran the fastest, we need to determine when the average speed was the greatest.
Let's rewrite the equation in terms of y as the number of miles and x as the time in minutes for the day with the maximum average speed.
Equation: y = (0.1x) + (0.125x)
Simplifying, we can combine the x terms:
y = 0.225x
Therefore, the equation is y = 0.225x, where y represents the number of miles and x represents the time in minutes for the day with the maximum average speed.
To find the day when you ran the fastest during the week, we need to compare the running speeds on Monday and Wednesday.
First, let's calculate the "miles per minute" for each day.
On Monday, you ran 4 miles in 40 minutes, so the running speed was:
Speed on Monday = Distance / Time = 4 miles / 40 minutes = 0.1 miles per minute
On Wednesday, you ran 2 miles in 16 minutes, so the running speed was:
Speed on Wednesday = Distance / Time = 2 miles / 16 minutes = 0.125 miles per minute
Since we are looking for the day when you ran the fastest, we need to find the day with the higher running speed.
Let's assign the variable x to the time in minutes (x = Time) and y to the number of miles (y = Distance).
Therefore, the equation for the day you ran the fastest can be written as:
0.1x = 0.125x
Now, let's solve this equation to find the value of x:
0.1x = 0.125x
0.125x - 0.1x = 0
0.025x = 0
x = 0 / 0.025
x = 0
The value of x is 0, which means you ran the same distance in the same amount of time on both Monday and Wednesday. This equation indicates that there was no difference in running speed between the two days.