When Dave walks to school, he averages $90$ steps per minute, and each of his steps is $75$ cm long. It takes him $16$ minutes to get to school. His brother, Jack, going to the same school by the same route, averages $100$ steps per minute, but his steps are only $60$ cm long. How long does it take Jack to get to school?
$\mathrm{(A) \ }14 \frac{2}{9} \text{minutes} \qquad \mathrm{(B) \ }15 \text{minutes}\qquad \mathrm{(C) \ } 18 \text{minutes}\qquad \mathrm{(D) \ }20 \text{minutes} \qquad \mathrm{(E) \ } 22 \frac{2}{9} \text{minutes}$
At $90$ steps per minute and $75 cm$ per step, Dave walks at a rate of $90\times75$ cm per minute, and with $16$ minutes, the distance Dave walks to school is $90\times75\times16$. Also, at $100$ steps per minute and $60$ cm per step, Jack walks at a rate of $100\times60$ cm per minute. Jack must walk $90\times75\times16$ cm, so it takes him $\frac{90\times75\times16}{100\times60}$ minutes. Canceling some of the factors, this comes out to $18 \text{minutes}, \boxed{\text{C}}$.