You could take your buckets, shampoo, pre wash, mitts and wheel brush to a buy time jet wash. I did this for years and still do now and it's great. £1/£2 ie the minimum to get things going with your pre wash and jet off for your 400 seconds allowing time to also part fill your bucket.
Wash the car as you would then normally taking as much time as you need. Then another £1/£2 to then finally jet the car off.
You could then pull the car round to the side to dry off or the drive home will do this for you - bingo. My Local BP is just £1 for a few minutes, so £2 is all that's needed.