Explanation
We can express Jay's painting rate as a fraction. It's
always useful to write the units in the fraction.
We want to know how long it takes to paint p rooms, so we want a fraction like this
with p in the numerator, not q. But we don't want to change the value
of fraction, because Jay's rate is not changing in this situation. So we can
multiply the fraction by 1 in the form of 
over :
The q's cancel
on top and we end up with p rooms,
just as we wanted. The time it takes to paint p rooms is evidently hours. We can check that it makes sense by
considering a case. If he paints at a rate of q=3 rooms per hour, and he's painting p=9 rooms, then it will take 
hours to paint nine rooms. It checks out.
The correct answer is (A).
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