A new set of car tires has a tread depth of 8 millileters. The tread depth decreases 0.12 millimeter per thousand miles driven. Write an equation that gives the tread depth as a function of the distance driven. Then predict what distance the tread depth will be 2 millimeters
To write an equation that gives the tread depth as a function of the distance driven, let's break down the given information step by step:
1. The initial tread depth is 8 millimeters.
2. The tread depth decreases by 0.12 millimeters per thousand miles driven.
Let's assume that "x" represents the distance driven in thousands of miles and "y" represents the tread depth in millimeters.
To find the equation, we need to find the relationship between the distance driven and the decrease in tread depth. Since the decrease is proportional to the distance driven, we can use the equation:
y = 8 - (0.12 * x)
In this equation, "8" represents the initial tread depth, and "(0.12 * x)" represents the decrease in tread depth as a function of the distance driven.
Now, let's predict the distance at which the tread depth will be 2 millimeters. We can set the tread depth (y) to 2 and solve for x:
2 = 8 - (0.12 * x)
To find x, we can rearrange the equation:
0.12 * x = 8 - 2
0.12 * x = 6
x = 6 / 0.12
x = 50
Therefore, when the tread depth reaches 2 millimeters, the distance driven would be 50 thousand miles.
To write an equation that gives the tread depth as a function of the distance driven, we can use the given information that the tread depth decreases by 0.12 millimeters per thousand miles.
Let's call the distance driven "d" in thousands of miles. The tread depth "t" can then be written as:
t = 8 - 0.12d
To predict the distance at which the tread depth will be 2 millimeters, we can substitute 2 for t in the equation and solve for d:
2 = 8 - 0.12d
Rearrange the equation to isolate d:
0.12d = 8 - 2
0.12d = 6
Divide both sides by 0.12:
d = 6 / 0.12
d = 50
Therefore, the tread depth will be 2 millimeters at a distance of 50,000 miles.