Answer
$11,800\ rpm$
Work Step by Step
The relationship of two rotating pulleys connected by a belt is:
(diameter of A)(rpm of A) = (diameter of B)(rpm of B).
Now, we have:
For pulleys A, B
$$
18\times 1200=5\times x\Longrightarrow x=\frac{18\times 1200 }{5}=4320\ rpm
.$$
Since the rpm of pulley B is equal to the rpm of pulley C, we have for pulleys C, D:
$$
15\times 4320=5.5\times x\Longrightarrow x=\frac{15\times 4320}{5.5}=11781.81\ rpm\approx 11,800\ rpm
.$$
