Tabernacle/ footwashings

One more point before we leave this subject of the Laver and that is the foot washing. Remember on the night before He was crucified how He girded Himself with a towel and taking a basin of water began to wash the feet of His disciples? Remember Peter's reaction when it was his turn? Let's turn to John 13:6-10, "
6 Then He came to Simon Peter. And Peter said to Him, “Lord, are You washing my feet?” 7 Jesus answered and said to him, “What I am doing you do not understand now, but you will know after this.” 8 Peter said to Him, “You shall never wash my feet!” Jesus answered him, “If I do not wash you, you have no part with Me.” 9 Simon Peter said to Him, “Lord, not my feet only, but also my hands and my head!” 10 Jesus said to him, “He who is bathed needs only to wash his feet, but is completely clean; and you are clean, but not all of you.”
The old testament priests had to wash both hands and feet but Jesus said to Peter "He who is bathed (or cleansed) needs only to wash his feet." So what is the connection and why the difference in these two instances? After all I have said that all these ceremonies in the Tabernacle service is a type pointing to the true worship and the cross of Christ. So why did they wash their hands as well as their feet in the O.T. and just their feet in the N.T? Jesus was illustrating a point here...we use our hands to work with....hands have to do with our works while feet has to do with our walk...there is nothing we can do with our works that will merit or earn salvation...not animal sacrifice , not keeping the law, nothing. All we can do is to walk in His steps and stay in His Word and that is the washing of the water of the Word that Paul speaks of in Ephesians. Our walk can become defiled and we need only our feet washed. It is a daily cleansing through the Word.