Just the last throw, as shown on the deed card:
If one "Utility" is owned rent is 4 times amount shown on dice. If both "Utilities" are owned rent is 10 times amount shown on dice.
"amount shown on dice", not "amount of all rolls this turn."
This is further reinforced on the Wiki:
If ONE Utility is owned, rent is 4x the number on the dice which ...
It is not in the rules. But on this page:
Utilities are the only properties without fixed rents, as rent depends
on the dice roll which landed the token on the property.
They only mention the dice roll, that landed the token on the property. So the rolls are not added.
The newest standard edition (post 2008) rules say:
If you land on an unowned Street, Railroad,
or Utility and you don’t want to buy it, the Banker
must auction it.
The Banker starts the auction by offering the
space to everyone for M$10.
Anyone can increase the bid by as little as M$1
(even the Banker and the player who originally
landed on the ...
This case only happens in UK edition since the card "Pay a ₤10 fine or take a Chance" only exists in UK edition. And the UK edition rules book say:
"Every time you either land on or pass "GO" while moving in the
direction of the arrow, you are paid £200 by the Bank."
So, you don't collect ₤200 when you pass GO backward.
My play group treat this as being bankrupt while owing the Bank.
The reason for this is that the player collectively owes every player $50. If the whole collective cannot be payed then the player is bankrupt owing everyone. There is no way to equally distribute the assets so handle the redistribution by Auction.
We don't pay the other players the $50. ...
There are indeed no instructions in the official rules on how to resolve multiple payments. A common mechanism in game design to handle such cases is to pay your debts in turn order. You go bankrupt to the player who you cannot pay.
Example: turn order is Alice, Bob, Charlie, Daniel and Eve. It's Alice's turn and she is instructed to pay $50 to each player....
According to a Ted-Ed article entitled
Here's how to win at Monopoly, according to math experts
... the average game of Monopoly takes about 30 turns per
So the answer to your question is 120 turns (4 players times 30 turns/player)