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
To find the day when you ran the fastest for the week, let's compare the average speed on Monday and Wednesday. Average speed is calculated by dividing the distance by the time taken.
On Monday:
Average speed = 4 miles / 40 minutes = 0.1 miles/minute
On Wednesday:
Average speed = 2 miles / 16 minutes = 0.125 miles/minute
Running faster means having a higher average speed. Therefore, we can compare the average speed equations for Monday (0.1x) and Wednesday (0.125x), where x represents the time in minutes.
0.125x > 0.1x
Simplifying the equation:
0.125x - 0.1x > 0
0.025x > 0
x > 0 / 0.025
x > 0
Since we know that x represents time in minutes, the equation is:
x > 0
This means that any positive value for x (time) will make Wednesday the faster day.
To write an equation with y as the number of miles and x as the time in minutes for the day you ran the fastest for the week, we need to compare the two given runs on Monday and Wednesday.
For Monday's run: y = 4 miles, x = 40 minutes
For Wednesday's run: y = 2 miles, x = 16 minutes
To determine the day you ran the fastest, we need to compare the speed (miles per minute) for both runs. The formula for speed is:
Speed = Distance / Time
For Monday's run:
Speed (Monday) = 4 miles / 40 minutes = 0.1 miles per minute
For Wednesday's run:
Speed (Wednesday) = 2 miles / 16 minutes = 0.125 miles per minute
Since Wednesday has a higher speed, it means you ran faster on that day.
Therefore, the equation for the day you ran the fastest for the week is:
y = 2x, where y represents the number of miles and x represents the time in minutes.
To find the day you ran the fastest, we can compare the average speed in miles per minute for each day. The equation to calculate the average speed is:
Average Speed = Distance / Time
Let's calculate the average speed for both days:
For Monday: Average Speed = 4 miles / 40 minutes = 0.1 miles per minute
For Wednesday: Average Speed = 2 miles / 16 minutes = 0.125 miles per minute
As we can see, the average speed on Wednesday is higher. Therefore, the equation to determine the day you ran the fastest would be:
0.125x > 0.1x
Simplifying the equation:
0.125x - 0.1x > 0
0.025x > 0
From the equation, we can conclude that the day you ran the fastest is Wednesday, as the average speed on Wednesday (0.125 miles per minute) is greater than the average speed on Monday (0.1 miles per minute).