[2 days left] What’s wrong with your cloud strategy? Learn why multicloud solutions matter with Nimble Storage.Register Now

x
Solved

# distance problem

Posted on 2004-09-17
Medium Priority
360 Views
This a problem that was found on a contest from 1996.

Two swimmers start out from opposite ends (red side and blue side) of a pool.  They cross each other for the first time at line PO which is 32 yards from the red side.  They reach the opposite ends, turn around and cross again at line RS which is 18 yards from the blue side.  Assuming that thye both travel at constant speeds, how many yards is it from the red side to the blue side?
0
Question by:djiangr
[X]
###### Welcome to Experts Exchange

Add your voice to the tech community where 5M+ people just like you are talking about what matters.

• Help others & share knowledge
• Earn cash & points
• 3
• 2
• 2

LVL 9

Accepted Solution

rjkimble earned 200 total points
ID: 12089885
Assuming the swimmers swim at a constant speed, we can conclude that the ratio of the distances traveled is constant. If D is the distance in question, then at the first crossing, the  red swimmer has swum 32 yards and the blue swimmer has swum D - 32 yards. At the second crossing, the red swimmer has swum D + 18 yards, and the blue swimmer has swum 2*D - 18 yards. Therefore:

32 / (D-32) = (D+18) / (2*D-18)

A little arithmetic follows:

32 * (2*D-18) = (D-32)*(D+18)

64*D - 576 = D^2 - 14*D - 576

D^2 - 78*D = 0

D = 78 yards

To verify, according to my computations, at the first crossing, the red swimmer has traveled 32 yards and the blue swimmer has traveled 46, a ratio of 16/23. At the second crossing, the red swimmer has traveled  96 yards and the blue swimmer has traveled 138, also a ratio of 16/23. The second set of distances is three times the first set.

The answer seems to be consistent with the conditions of the problem, so I'll guess I got it right. Here's hoping I haven't screwed up the arithmetic somewhere. :-)
0

LVL 7

Expert Comment

ID: 12089957
Let L = length of pool (the answer you seek)
t1 = time for both swimmers to cross at PO
t2 = time for both swimmers to cross at RS
vr = speed of swimmer starting at red side
vb = speed of swimmer starting at blue side

Write equations for distance = speed * time

Distance travelled by swimmer from red side to crossing at PO:
32 = vr t1
Distance travelled by swimmer from blue side to crossing at PO
L - 32 = vb t1

Distance travelled by swimmer from red side from crossing to crossing at RS
L + 18 = vr t2

Distance travelled by swimmer from blue side to crossing at RS
L + L - 18  = vb t2

The first pair of equations give vb/vr = (L - 32)/32
Second pair gives vb/vr = (2L - 18)/(L + 18)

So (L - 32)/32 = (2L - 18)/(L + 18)

Solve for L to get the answer...
0

LVL 7

Expert Comment

ID: 12089971
I was writing my post while rjkimble submitted his.  I agree with his analysis.
0

LVL 9

Expert Comment

ID: 12090522
Well, this is pretty simple stuff! :-)

It's a Saturday night and I'm bored....
0

LVL 6

Expert Comment

ID: 12095120
shorter way :

t1 : 1st meeting , red swimmer passed 32 , both swimmers passed d
t2 : 2nd meeting , red swimmer passed d+18 , both swimmers passed 3*d (!!!)

since sum of velocitied not changed as well as each swimmer's speed =>
t2 = 3*t1

d+18 = 3*32 (the way red swimmer passed  until t2 , is 3 times the way he passed until t1)

d+18 = 96 => d=78 yards

tal
0

LVL 9

Expert Comment

ID: 12096759
tal: sorry to hear about the funeral.

Very nice observation -- even brilliant. At first I didn't see your point, but after thinking about it, it's a very nice observation. If I could give the points to you, I would. Some solutions are better than others, and in this case your solution is better.
0

LVL 6

Expert Comment

ID: 12099979
rj ,

not for the points .

my wife is teaching math at high school and I wrote this question down for her as a very good one ,

I recommended her to give points for a good solution :

1) solve the question using square equation - 10 points ,
2) not using square equations - 15 points ...

"c u" later in other Questions , BTW your profile is realy something .

tal
0

## Featured Post

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

How to Win a Jar of Candy Corn: A Scientific Approach! I love mathematics. If you love mathematics also, you may enjoy this tip on how to use math to win your own jar of candy corn and to impress your friends. As I said, I love math, but I gu…
When we purchase storage, we typically are advertised storage of 500GB, 1TB, 2TB and so on. However, when you actually install it into your computer, your 500GB HDD will actually show up as 465GB. Why? It has to do with the way people and computers…
Although Jacob Bernoulli (1654-1705) has been credited as the creator of "Binomial Distribution Table", Gottfried Leibniz (1646-1716) did his dissertation on the subject in 1666; Leibniz you may recall is the co-inventor of "Calculus" and beat Isaac…
I've attached the XLSM Excel spreadsheet I used in the video and also text files containing the macros used below. https://filedb.experts-exchange.com/incoming/2017/03_w12/1151775/Permutations.txt https://filedb.experts-exchange.com/incoming/201…
###### Suggested Courses
Course of the Month14 days, 21 hours left to enroll