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

`(1)/(160) \ inches`

Explanation:

The computation of the thickness of tire rubber for every lost 1,000 driven is shown below:

Data provided in the question

Inches of tread =
`(10)/(23)`

In case of replaced =
`(2)/(3)`

Based on the above information

Now in 40,000 miles, the ratio is

`= (10 - 2)/(32) \\\\ = (1)/(4)`

And for every 1,000 miles driven, the thickness is

`= (1)/(4 * 40,000) * 1,000 \\\\ = (1)/(160) \ inches`

hence, the thickness of tire rubber is
`(1)/(160) \ inches`