Many tires come with 13/32 inch of tread. The first 2/32 inch wears off quickly(say during the first 1000miles). From then on the tire wears uniformly. A tire is considerd "worn out" when on 2/32 inch of tread is left.

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

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?

a. (13-2)/32 =

b. @1000 it had 11/32. @20000 it had 5/32.

So after 19,000 it lost 6/32.

It needs to lose another 3/32 to be "worn out".

You should be able to see the number of miles from that.

a. To find out how many 32nds of an inch of usable tread a tire has after 1000 miles, we need to subtract the amount that wears off quickly (2/32 inch) from the total amount of tread (13/32 inch).

So, 13/32 inch - 2/32 inch = 11/32 inch.

Therefore, after 1000 miles, the tire will have 11/32 inch of usable tread remaining.

b. To find out how many total miles the tire should last before it is considered worn out, we can set up a proportion using the given information.

Given:
The tire has traveled 20,000 miles and has 5/32 inch of tread remaining.
The tire is considered worn out when only 2/32 inch of tread is left.

Let's set up the proportion:

(20,000 miles) / (5/32 inch) = (x miles) / (2/32 inch)

To solve for x, we can cross-multiply and then solve for x:

(20,000 miles) * (2/32 inch) = (5/32 inch) * (x miles)

400,000 miles = 5x

Divide both sides by 5:
400,000 miles / 5 = 5x / 5

80,000 miles = x

Therefore, the tire should last approximately 80,000 miles before it is considered worn out.