The amount of tread left on a tire varies inversely as the number of miles the tire has traveled. A tire that has traveled 40,000 mi has $\frac { 5 } { 8 }$ in. of tread left. How much tread will be left on a tire that has traveled 19,000 mi ?
A) $\frac { 25 } { 19 } \text { in. }$
B) $\frac { 19 } { 25 } \text { in. }$
C) 64,000 in.
D) $\frac { 1 } { 64000 } \text { in. }$

Question

The amount of tread left on a tire varies inversely as the number of miles the tire has traveled. A tire that has traveled  40,000 mi has  $\frac { 5 } { 8 }$  in. of tread left. How much tread will be left on a tire that has traveled  19,000 mi ?
A) $\frac { 25 } { 19 } \text { in. }$
B) $\frac { 19 } { 25 } \text { in. }$
C)  64,000 in.
D) $\frac { 1 } { 64000 } \text { in. }$

Quizplus · Accepted Answer

The relationship between tread left (T) and miles traveled (M) is inversely proportional, so $T = k/M$, where k is a constant. For a tire with 40,000 miles and $\frac{5}{8}$ inch of tread, $k = T \times M = \frac{5}{8} \times 40,000$. For 19,000 miles, using the same k, solve for T to find the tread left. The correct calculation leads to $\frac{25}{19}$ inches of tread left.

The Amount of Tread Left on a Tire Varies Inversely 58\frac { 5 } { 8 }85​

The Amount of Tread Left on a Tire Varies Inversely $\frac { 5 } { 8 }$