# A cyclist rides from one point to another over five days. On the first day............How many miles has she travelled?

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A cyclist rides from one point to another over five days.

On the first day she covers one eighth of the total distance.

The next day she covers one quarter of what is left.

The following day she covers two fifths of the remainder

and on the fourth day half of the remaining distance.

The cyclist now has 25 miles left.

How many miles has she travelled?

posted Oct 18, 2019

~127 miles

d- total distance, d1 to d5- travel per day, from day1 to day5
d=d1+d2+d3+d4+d5=d1+d2+d3+d4+25=d1+d2+d3+25+25
d1=d*1/8, reminder=r1=d-d1=d*7/8
d2=1/4*r1=1/4*d*7/8=d*7/32, r2=r1-d2=d*7/8-d*7/32=d*21/32
d3=r2*2/5=d*21/32*2/5=d*21/80, r3=r2-d3=d*21/32-d*21/80=d*63/160
d4=r3/2=25 miles --> r3=50 --> d*63/160=50 -->
--> d=50*160/63 = ~127 miles

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