Wald on the Reshuffling Deck

A deck holds 60 cards labelled 1 to 60 plus 40 jokers, shuffled uniformly at random. Priyanshu draws one card per second off the top. Drawing a numbered card $x$ removes it from the deck and adds $x$ to a set $S$. Drawing a joker triggers a check: if $S \neq {1, 2, \dots, 60}$ he returns every card, reshuffles all 100 (instantly, and $S$ is kept), and carries on; if $S = {1, 2, \dots, 60}$ the game ends.

Simulation puts the expected number of rounds, each ending the moment a joker turns up, at 188.195. On average, how many seconds does the game last?

Answer format: enter an integer.