The circumference of the wheel is $2.5\pi$ feet. At $45$ miles per hour, we are travelling at $\frac{(45)(5280)}{60}$ feet per minute.
So if $s$ is the number of revolutions per minute, we have $(2.5\pi)s=\frac{(45)(5280)}{60},$ and therefore $s=\frac{(45)(5280)}{(60)(2.5\pi)}.$ The rest can be done by calculator.
The other problem involves more or less the same ideas, but is a little easier. The circumference of the tire is $78\pi$ cm. At $600$ rpm, we travel $(78\pi)(600)$ cm per minute. This is $(78\pi)(600)(60)$ cm per hour. To convert to km per hour, divide by the number of cm in $1$ km, which is $100000$.