A hiker walks from one town to another.
On the first day she covers one eighth of the total distance, the next day she covers one third of what is left.
The following day she covers one quarter of the remainder and on the fourth day half of the remaining distance.
She now has 10 miles remaining.
How far has she travelled?
Dark Side of the Moo
13 years ago
It depends on what shoes she is wearing.
ReplyDeleteMy answer is---250/7 miles
ReplyDeleteIs that correct?
am not certain. the answer hasn't been published yet.
ReplyDeleteSo far I think that it's about 36 miles? are there any maths people out there?
Here is the way I used to solve the puzzle--
ReplyDeleteThe first day the remainder was 7/8 of all. The next day the remainder became 2/3 of 7/8. The following day the remainder became 3/4 of 2/3 of 7/8. And the fourth day the remainder became 1/2 of 3/4 of 2/3 of 7/8.
So, the remainder is--
7/8×2/3×3/4×1/2=7/32
Supposed she travelled x miles,
x:10=(32-7):7
7x=25×10
x=250/7 A. 250/7 miles
I am good at math, and teaching to junior high school students privately, but I want to know if that is correct or not.
Are there really any maths people out there?
I am still pretty certain that it is 36 miles. I have gone through your maths and see what you have done. I looked at it differently and worked backwards:
ReplyDeleteI will explain what I have done in more detail when I have a few minutes free.
My dear Dad (who is a qualified maths teacher and personal tutor) says it is 35 and 5/7
ReplyDeletemiles .... the total distance being 45 and 5/7 miles
I don't know how he worked it out though..
Here is what i came up with...
ReplyDeleteStarted with 44.5 miles
Miles Traveled Run. Total
Each Day 44.5
1/8 5.56250000 40.00000000
1/3 13.33333333 26.66666667
1/4 6.66666667 20.00000000
1/2 10.00000000 10.00000000
35.56250000 Miles Traveled