Find the product of $\frac{12 rad}{1 min} * \frac{1 rev}{2\pi rad} * \frac{60 min}{1 hr}$

Question

For some reason, this answer got marked as incorrect:

$\frac{60 min}{1 hr} = 1$

$\frac{12 rad}{1 min} * \frac{1 rev}{2\pi rad} = \frac{12 rad}{1 min} * \frac{\frac{12 rev}{2\pi}}{12rad} = \frac{6}{\pi} rev/min$

Can someone tell me what mistakes I made?

*Rev = Revolutions *The answer should contain a unit.

Answer 1

These could all be units of plane angle, not time, in which case, use the given conversions:

$1\text{ hour angle}=15^\circ\\60\text{ minutes}=1^\circ\\\pi\text{ rad}=180^\circ\\1\text{ rev}=360^\circ$

Your final answer should be a dimensionless constant.

Answer 2

In a problem like this there are two steps:

• Do arithmetic with the numerals to determine the numeral part of the answer,
• Cancel units to determine the units part of the answer.

The arithemetic part gives $$\frac{12 \times 1 \times 60}{1 \times 2\pi \times 1} = \frac{360}{\pi} $$ For the units part, after cancelling radians and minutes what's left is $\frac{rev}{hr}$, leading to a final answer of $$\frac{360}{\pi} \frac{rev}{hr} $$