Question 935625
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.