SOLUTION: I am supposed to use the Ratio Method Please Help. Many tires come with 13/32 inch of tread on them. The first 2/32 inch wears off quickly (say during the first 1000 miles). Fro

Algebra ->  Geometry-proofs -> SOLUTION: I am supposed to use the Ratio Method Please Help. Many tires come with 13/32 inch of tread on them. The first 2/32 inch wears off quickly (say during the first 1000 miles). Fro      Log On


   



Question 936383: I am supposed to use the Ratio Method Please Help.
Many tires come with 13/32 inch of tread on them. The first 2/32 inch wears off quickly (say during the first 1000 miles). From then on the tire wears uniformly and more slowly. A tire is considered “worn out” when only 2/32 inch of tread is left.

a. How many 32nds of an inch of useable tread does a tire have after 1000 miles?

b. A tire has traveled 20,000 miles and has 5/32 inch of tread remaining. At this rate, how many total miles should the tire last before it is considered worn out?

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Many tires come with 13/32 inch of tread on them.
The first 2/32 inch wears off quickly (say during the first 1000 miles).
From then on the tire wears uniformly and more slowly.
A tire is considered “worn out” when only 2/32 inch of tread is left.
:
a. How many 32nds of an inch of useable tread does a tire have after 1000 miles?
The useable tread is after the first 2/32 up to the last 2/32, therefore
13%2F32+-+2%2F32+-+2%2F32 = 9%2F32
b. A tire has traveled 20,000 miles and has 5/32 inch of tread remaining.
At this rate, how many total miles should the tire last before it is considered worn out?
Let t = total miles, only 3/32 is useful miles
t%2F20000 = %289%2F32%29%2F%283%2F32%29
We know that 9/32 divided by 3/32 = 3, so a simple equation
t%2F20000 = 3
t = 60,000 miles before it is worn out