Given:
A standard tire has 10/32 inches of tread.
The tire needs to be replaced when only 2/32 inches of tread remains left.
Here the tire is needed to be replaced after 40,000 miles.
To find:
The thickness of tire rubber lost every 1,000 miles.
Step-by-step solution:
According to the question,
The tire is replaced when only 2/32 inches of tread remain left.
The new tire has 10/32 inches of tread.
Thus tire needs to loose:
10/32 - 2/32 = 8/32 inches of tread.
This means upon traveling for 40,000 miles, 8/32 inches of tread is lost.
So their ratio equals:
40,000 = k (8/32)
k = 40,000 × 32 / 8
k = 40,000 × 4
k = 1,60,000
So to calculate for 1000 miles:
1000/x = 1,60,000
1/x = 1,60,000 / 1000
1/x = 160
x = 1 / 160 inches
Thus we can say for every 1000 miles, 1 / 160 inches of tread is lost.