Hey OP, the pipe that drains your dishwasher is generally connected to your sink.
That pipe is only so big in terms of cubic inches, so if you're running your faucet AND your dishwasher, stuff usually backs up.
Plumbing code calculated/engineered for diswasher allowance. The connection is up stream of the garburator to help cleaning out the piping and p-trap, unless there is a clog/partially clog pipe, or an incorrectly install riser that doesn't have sufficient sud zone distance for the clothwasher/dishwasher from above riser so that there is an air lock in the piping (vent).
The length of time it takes for water to appear in the sink can help determine how much snake you need.
Size of pipe will determine how much water it can hold per foot of run. If you know how much water volume you get from the tap, then run the water while a stopwatch is active. Do the math.
I had a blockage this summer from something. It took about twenty seconds for water to appear in the sink. The 25 foot snake was fully doled out and the blockage disappeared.
LOL, length of time * what? == distance? == perhaps it is quasi math that you are doing.
Kitchen sink trap arm can be 1 1/2", or 2" and can be up to 8' long. The riser that the trap arm connected to can be a 1 1/2" to 4", and the horizontal branch can be 2" to 4", building drain can be 3" or 4", and clog also pass water at an unknown rate. How the hell are you going to figure it out how long the pipe is even if you time the sink to fill a gallon bucket?
[edit]
Oops, almost forgot, building code call for minimum of 2" horizontal branch for kitchen sink, while wash basin and stand pipe can be as little as 1 1/4" (however, most if not all do not install 1 1/4" piping, because it cost more than the standard 1 1/2" pipe).