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 $18 \text{minutes}, \boxed{\text{C}}$.