Astronomy Class question

Question

When new, a standard tire has 10/32 inches of tread. When only 2/32 inches of tread remains, the tire needs to be replaced. If this occurs after 40,000 miles, what thickness of tire rubber is lost every 1,000 miles driven? Give your answer in fractions of an inch.

Answer 1

New: 10/32"

Ready to be replaced: 2/32"

This means that the tire has to loose: 10/32" - 2/32" = 8/32" (or 1/4" but the problem seems to keep in terms of 1/32", so we will stick to that)

We can go 40,000 miles before we loose 8/32, so the question is, how much tread do we loose in 1000 miles?

Easiest way to do this is set up a proportion:

miles/tread lost = miles/tread lost

40,000miles/(8/32")=1000miles/(x")

(40,000miles)(8/32")=(1000miles)(x")

x=((8/32")(1000miles))/(40,000miles)

x=(250)/(40000)

x=.00625" which is 1/160" => so for every 1000 miles, the tire looses 1/160" of tread.

To check, simply multiply 1/160" by 40 to see if after 40000 miles, you get the 1/4" we were told the tire looses:

(1/160)(40)=(40/160)=(4/16)=1/4. So we know that if the tire looses 1/160" every 1000 miles, after 40,000 miles, it will have lost 1/4" (or 8/32"), which is the amount a new tire needs to loose to be replaced.

Timmy