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Puzzle Details

A man drove from Aardvark to Beeville.

On the first day he travelled 1/3 of the distance.

On day two he travelled 1/2 of the remaining distance.

On day three he travelled 2/3 of the remaining distance.

On day four, after covering 3/4 of the remaining distance, he was still 5 miles away from Beeville.

How many miles had he covered so far?

The total trip was 180 miles. Working backwards:

Day 4: travelled 3/4 leaving 5 miles, which means that 5 miles is 1/4, so 20 miles were left at the start of Day 4.

Day 3: travelled 2/3 leaving 20 miles, which means that 20 miles is 1/3, so 60 miles were left at the start of Day 3.

Day 2: travelled 1/2 leaving 60 miles, which means that 60 miles is 1/2, so 120 miles were left at the start of Day 2.

Day 1: travelled 1/3 leaving 120 miles, which means that 120 miles is 2/3, so 180 miles were left at the start of Day 1.

Of the 180 miles overall, 175 were covered in the 4 days. QED.

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