SOLUTION: I know I am suppose to use the method of Ratios but this is so confusing to me please help! Many tires come with 13/32 inch of tread on them. The first 2/32 inch wears off quic

Question 935625: I know I am suppose to use the method of Ratios but this is so confusing to me 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 Theo(13342) (Show Source): You can put this solution on YOUR website!
you start at 13/32 of an inch of tread.

after 1000 miles, you lost 2/32 of an inch of tread, so you have 13/32 - 2/32 = 11/32 of an inch of tread left.

after 20000 miles, you have 5/32 of an inch of tread left.

from 1000 miles to 20000 miles, you lost 11/32 - 5/32 = 6/32 of tread after traveling an additional 19000 miles.

the tire is worn when you get to 2/32 of an inch of tread left.

from 5/32 to 2/32 is 3/32.

you wear off another 3/32 of tread between 5/32 of an inch of tread on your tire and 2/32 of an inch of your tire.

you know that you wore off 6/32 of tread in 19000 miles.

that's between 1000 miles and 20000 miles that we calculated earlier.

your ratio will be:

(6/32) / 19000 = (3/32) / x

x will represent the additional number of miles you travel before the tire is declared worn out.

multiply both sides of this equation by x and divide both sides of this equation by (6/32) and you get:

x = (3/32) * 19000 / (6/32)

since 19000 / (6/32) is the same as 19000 * (32/6), your equation becomes:

x = (3/32) * (32/6) * 19000 which becomes:

x = 3/6 * 19000 which becomes:

x = 9500 miles.

your tire will be declared worn out in an additional 9500 miles.

the total miles the tire will have traveled is 1000 + 19000 + 9500 which is equal to 29500 miles.

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