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Let the Good Times Roll

You've decided to drive cross-country to New Orleans for Jazz Fest (and some sweet, sweet Creole cookin').

On Day 1: You make good time, travelling halfway there.

On Day 2: You stop for lunch and only travel one-third of the remaining distance.

On Day 3: You get stuck in the mud, but you make it three-quarters of the remaining distance.

On Day 4: You oversleep and only make it another half of the remaining distance.

There are now 10 miles left to go before you hit the Big Easy. Exactly how far have you traveled on your way to laissez les bons temps rouler?

Disclaimer: I am not the original author, I just wanted to share this puzzle.

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You have traveled:

230 miles and have 10 left to go

Because:

Working backwards, on Day 4 you went half of what was left and have 10 miles remaining, so 10 miles.
Day 3 was $3/4$ of the remainder, leaving 20, so you went 60.
Day 2 was $1/3$ of the remainder, leaving 80, so you went 40.
Day 1 was half, leaving 120, so you went 120.

Summing:

120 + 40 + 60 + 10 = 230

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