To hasten to a destination.
"run up" is correct and usable in written English. You can use it to refer to an activity that is done quickly or that has been done over a short period of time. For example, "He ran up the stairs in record time.".
Run up the middle?
Overdraft fees can run up to $40.
"We have run up substantial legal costs.
Any trying to run up the aisle.
Now the dollar run-up is wider.
"He did the same run-up".
In the run-up to the announcement.
I love the desktop app, it’s always running on my Mac. Ludwig is the best English buddy, it answers my 100 queries per day and stays cool.
Cristina Valenza
Retail Lead Linguist @ Apple Inc.