Last week I drove from Aardvark to Beeville.
On the first day, I travelled 1/3 of the starting distance.
On day two, I travelled 1/2 of the remaining distance.
On day three, I travelled 2/3 of the remaining distance.
At the end of day four, after travelling 3/4 of the remaining distance, I was still 5 miles away from Beeville.
How many miles had I travelled so far?
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Answer
175 miles.
The total distance was 180 miles, but as I still had 5 miles to go, the required answer is 175 miles.
Reasoning
Let's try working backwards.
Day 4: I travelled 3/4, which means that the other 1/4 was 5 miles – so 20 miles were left at the start of day four.
Day 3: I travelled 2/3, which means that the other 1/3 was 20 miles – so 60 miles were left at the start of day three.
Day 2: I travelled 1/2, which means that the other 1/2 was 60 miles – so 120 miles were left at the start of day two.
Day 1: I travelled 1/3, which means that the other 2/3 was 120 miles – so 180 miles were ahead at the start of day one.
The full distance was therefore 180 miles, but we were asked how many miles I had travelled so far, and as I still had 5 to go the answer is 175 miles.
Double-Checking
Start distance: 180 miles.
Day 1: I travelled 1/3 of the distance (60 miles), leaving 120 miles.
Day 2: I travelled 1/2 of the distance (60 miles), leaving 60 miles.
Day 3: I travelled 2/3 of the distance (40 miles), leaving 20 miles.
Day 4: I travelled 3/4 of the distance (15 miles), leaving 5 miles.
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