What must be done in order to solve for the unknown variable?

I don't know if this is 100% correct...but i think this is how you would solve this problem!!!

OOO

We all know that a well is circular. So, First, lets find out the circumference of the wheel.

Given :
radius = 10 feet
π = 22 / 7
We know,
Circumference = 2πr
                      = 2 × (22 / 7) × 10
                      = 62.9 ft.

Now,
One revolution means the wheel has covered a distance equal to its circumference. So, 22 revolutions per minute means that the wheel is covering 22 times its circumference in 1 minute. So, Lets convert the revolution to feet.

Given,
The wheel is travelling at 22 revolutions per minute.
                                 =  22 * Circumference per minute
                                 =  22 * 62.9 ft. per minute
                                 = 1383.8 ft. per minute
Now, that we know how much feet it is travelling in 1 minute, we can easily find how much it takes it to travel 10 feet. 

Using unitary method,
The wheel travels 1383.8 ft. in 1 minute
The wheel travels 1383.8 ft. in 60 seconds.
The wheel travels 1 ft. in (60 /  1383.8) seconds.
The wheel travels 10 ft. in (60 /  1383.8) * 10 seconds.
                                      = 0.4 seconds

So, the answer is 0.4 seconds. Of course...the answer is rounded!!