Cross section of a river that is 3km wide & 30m deep?

You can use whatever units you wish as long as they are converted correctly. What you wrote works (3,000m * 30m = 90,000m^2) but you could also do (3km * .03km = .09 km^2) and be just as correct. If it helps, here is the full conversion…

3 km * (1000 m / 1 km ) * 30 m = 90,000 m^2

Think of m and km as variables in a sense. Since there is m*m it becomes meters squared and km/km the kilometers cancel out. The same works for km…

3 km * 30 m * (1 km / 1000 m ) = .09 km^2

I just posted that as another example of conversion since you will want to use 90,000 m^2 for part two. In order to convert any type of units, you must multiply it by the fraction which contains both what you are converting it to and the current unit. The current unit goes on the bottom and the unit you are converting to goes on top. In the example, since 1 km = 1000 m, you are effectively multiplying by one so it is ok to do mathematically.

As for the second part of your problem, you can start by figuring out what units you want. Since it is velocity, the common measurements are m/s or kph. Kph (kilometers per hour) would require more unit converting so go with m/s and therefore use the first result (90,000 m^2) rather than the second (.9 km^2).

( 22,000 m^3 / s ) / ( 90,000 m^2 ) / = .2444 m/s

Since your final value needs m on top and s on the bottom, you will have to divide the 22,000 by 90,000. Notice that m^3/s is close to m/s. By dividing it by 90,000 m^2 the m^3 becomes m (or m^1 if you want to think of it that way). Like I mentioned earlier, think of it as a variable and apply the basic exponential rules.

I hope that helps, it is a lot easier to read/understand when it is written out on paper.