# A group of cyclists ride from one town to another. On the first day they cover one.........How far have they travelled?

+1 vote
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A group of cyclists ride from one town to another.

On the first day they cover one third of the total distance. The next day they cover one quarter of what is left. The following day they cover two fifths of the remainder and on the fourth day half of the remaining distance.

The cyclists now have 20 miles left.

How far have they travelled?

posted Sep 8, 2017

How far have they traveled?
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Appears that the question is asking how far they have traveled at the end of day 4 when they still have 20 miles to go.
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The answer is 113 1/3 miles traveled by the end of day 4.
Total distance of the planned trip is 133 1/3 miles.
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Working backwards from the end of day 4.
There are 20 miles left.
20 miles = 1/2 of what remained at end of day 3.
So at end of Day 3 they had 40 miles left (20 divided by 1/2)
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40 miles = 3/5 of what was left at end of day 2.
So at end of day 2 they had 66.2/3 miles left. (40 divided by 3/5)
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66 2/3 miles = 3/4 of what was left at end of day 1.
So at end of Day 1 they had 88 8/9 miles left (66 2/3 divided by 3/4)
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88 8/9 miles = 2/3 of start of day 1
So at start of day 1 they had 133 1/3 miles to go.
This represents the total distance of the planned trip.
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So at end of day 4 they still had 20 miles left.
133 1/3 - 20 = 113 1/3 miles traveled.

they have traveled 113,3 miles

answer Dec 14, 2017 by anonymous

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