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# How many times Swimmers meet?

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How many times Swimmers meet? [#permalink]  10 May 2010, 02:55
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Two swimmers start at opposite ends of a pool 89 feet long. One person swims at the rate of 19 feet per minute and the other swims at a rate of 53 feet per minute. How many times will they meet in 33 minutes?

A.13
B.11
C.10
D.8
E.5
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Re: How many times Swimmers meet? [#permalink]  10 May 2010, 08:55
Hussain15 wrote:
Two swimmers start at opposite ends of a pool 89 feet long. One person swims at the rate of 19 feet per minute and the other swims at a rate of 53 feet per minute. How many times will they meet in 33 minutes?

A.13
B.11
C.10
D.8
E.5

http://www.brainmass.com/homework-help/ ... eory/11370
Before searching for the result, I got 13. But after thinkin' for a while, both the man on that site and I had a same mistake: we assume that two swimmers ALWAYS meet each other when they swim in different directions. We must prove that the swimmer with the rate of 53 feet/min never passes the other (when they swim toward a same end of the pool or swim in the same direction). But that happened.
Correct me if I'm wrong, please
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Re: How many times Swimmers meet? [#permalink]  10 May 2010, 08:57
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Hussain15 wrote:
Two swimmers start at opposite ends of a pool 89 feet long. One person swims at the rate of 19 feet per minute and the other swims at a rate of 53 feet per minute. How many times will they meet in 33 minutes?

A.13
B.11
C.10
D.8
E.5

Good Question..!

After spending alot of time I am still not sure whether I am right here or not...!

Anyway,

Total number of laps by slow swimmer in 33 minutes = $$\frac{33}{time for one lap}$$ = $$\frac{33}{(89/19)}$$ = $$\frac{33}{4.68}$$ =$$7$$ ( approx )

total number of laps by fast swimmer = $$\frac{33}{time for one lap}$$ = $$\frac{33}{(89/53)}$$ = $$\frac{33}{1.68}=$$$$19.68=$$$$20$$ ( approx )

Now, The number of laps the fast swimmer completes when the slow swimmer completes one lap = $$\frac{4.68}{1.68}$$= 2.7
During these 2.7 laps the fast swimmer will meet the slow swimmer thrice ( one when they are swimming in opposite direction second when they are swimming in the same direction and third when again they are swimming in opposite direction)

Total number of times when they will meet = $$\frac{Total number of laps completed by the fast swimmer in 33 minutes *3}{2.7}$$ $$= \frac{19.68*3}{2.7}= 21$$

But I see thats not an option ..!
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Re: How many times Swimmers meet? [#permalink]  10 May 2010, 09:01
DavidArchuleta wrote:
Hussain15 wrote:
Two swimmers start at opposite ends of a pool 89 feet long. One person swims at the rate of 19 feet per minute and the other swims at a rate of 53 feet per minute. How many times will they meet in 33 minutes?

A.13
B.11
C.10
D.8
E.5

http://www.brainmass.com/homework-help/ ... eory/11370
Before searching for the result, I got 13. But after thinkin' for a while, both the man on that site and I had a same mistake: we assume that two swimmers ALWAYS meet each other when they swim in different directions. We must prove that the swimmer with the rate of 53 feet/min never passes the other (when they swim toward a same end of the pool or swim in the same direction). But that happened.
Correct me if I'm wrong, please

I saw that link but some how I am not able to understand how did he made that calculation that for the second they have to meet it has to be 3 times the length of the pool and then 5 times ..

I think they will meet whenever thy cross each other , ( whether they are swimming in opposite dierction or same direction)
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Re: How many times Swimmers meet? [#permalink]  10 May 2010, 09:45
In this case:-
1.Length of the pool is quite small compared to speed of fast swimmer(s=53f/m) .
2.Difference between speeds of two swimmers is large.

Considering above statements faster swimmer passes slower swimmer more than twice during single lap completed by slower swimmer, and this skews the otherwise simple relative speed problem.
Slower swimmer(s=19 f/m) takes approximately 4.6min to finish one lap, in the same time faster swimmer finishes 2.7 laps.
Hence faster swimmer crosses slower swimmer head on , tail on and again head on while the slower swimmer is yet to complete first lap.
Therefore relative speed continues to alternate between 72 & 34 depending upon the direction in which the swimmers are swimming at a particular instant.
For rough estimation we consider that faster swimmer meets slower swimmer, thrice in each lap completed by slower swimmer.
Then number of times they will meet = 33/4.6*3 = approximately 21 times.
Actually it will be few times lesser, if we consider 33/4.6*2.7.

But there is no option greater than 13...
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Re: How many times Swimmers meet? [#permalink]  10 May 2010, 19:16
nitishmahajan wrote:

I saw that link but some how I am not able to understand how did he made that calculation that for the second they have to meet it has to be 3 times the length of the pool and then 5 times ..

I think they will meet whenever thy cross each other , ( whether they are swimming in opposite dierction or same direction)

Yeah, he's wrong, because he just counts the number of time 2 swimmers meet when they come in opposite directions.
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Re: How many times Swimmers meet? [#permalink]  11 May 2010, 03:24
So whats the conclusion here. Whats the decided answer?
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Re: How many times Swimmers meet? [#permalink]  11 May 2010, 07:26
Hussain15 wrote:
Two swimmers start at opposite ends of a pool 89 feet long. One person swims at the rate of 19 feet per minute and the other swims at a rate of 53 feet per minute. How many times will they meet in 33 minutes?

A.13
B.11
C.10
D.8
E.5

Bunuel ....!

Any thoughts for this one ??
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Re: How many times Swimmers meet? [#permalink]  11 May 2010, 07:56
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IMO 13 - A

Their relative speed = 53 + 19 = 72

They will meet first time in $$\frac{89}{72}$$minutes.
After they will cross each other they will have to cover 2*89 to meet again.
Thus for the second time they will meet in $$2*\frac{89}{72}$$ minutes

Let n be the number of time they meet after crossing once

equation is

$$\frac{89}{72} * + \frac{89}{72} *(2n) <= 33$$

$$2n+1 <= 33* \frac{72}{89} < 33* \frac{72}{88} = 27$$

=> 2n+1 <= 26.something
=> 2n <= 25.something
=> n =12

this gives n = 12, so final result n+1 = 13

Whats the OA
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Re: How many times Swimmers meet? [#permalink]  11 May 2010, 08:21
gurpreetsingh wrote:
IMO 13 - A

Their relative speed = 53 + 19 = 72

They will meet first time in $$\frac{89}{72}$$minutes.
After they will cross each other they will have to cover 2*89 to meet again.
Thus for the second time they will meet in $$2*\frac{89}{72}$$ minutes

Let n be the number of time they meet after crossing once

equation is

$$\frac{89}{72} * + \frac{89}{72} *(2n) <= 33$$

$$2n+1 <= 33* \frac{72}{89} < 33* \frac{72}{88} = 27$$

=> 2n+1 <= 26.something
=> 2n <= 25.something
=> n =12

this gives n = 12, so final result n+1 = 13

Whats the OA

Gurpreet,

This is what the confusion is ... you are assuming that they will only meet when they are swimming in the opposite directions Right ?

But in my opinion they would meet even if they are swimming in the same direction,

For e.g for the first time they will meet in 89/72 mins but the fast swimmer will again cross the slow swimmer when the slow swimmer is still completing his lap ( slow swimmer time to complete one lap = 4.68 , fast = 1.68)
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Re: How many times Swimmers meet? [#permalink]  11 May 2010, 08:25
In the question it is mentioned they start from two opp ends of 89 feet long pool.

IMO they will be opp only on length wise.
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Re: How many times Swimmers meet? [#permalink]  11 May 2010, 09:54
It wont help even if they start from same end as the relative speed is not constant.
I mean starting from same end the relative speed will be 34fpm initially, however once the faster swimmer completes the lap relative speed will become 72fpm and it will keep on alternating depending upon the relative direction(towards/opposite to each other), hence problem cannot be solved applying simple relative speed concept.

Only an approximate answer can be reached..
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Re: How many times Swimmers meet? [#permalink]  17 Jun 2010, 13:41
gsothee wrote:
It wont help even if they start from same end as the relative speed is not constant.
I mean starting from same end the relative speed will be 34fpm initially, however once the faster swimmer completes the lap relative speed will become 72fpm and it will keep on alternating depending upon the relative direction(towards/opposite to each other), hence problem cannot be solved applying simple relative speed concept.

Only an approximate answer can be reached..

I still believe 13 is the right answer. Just look at my solution above. Imagine they are always moving towards each other. We have to find in 33 minutes what distance they can cover together.

Since they are at opp sides, they will cover 89 feet 1st time they meet. For second time they will have to cover 2 times 89 and so on. So every time they will have to cover 2*89 distance except for the 1st time.
so the total distance covered will be 89 + 89*2 + 89*2 --------------
this total distance should be <= 33*72

=> 89 + 89*2n <= 33*72 which gives n = 12

so total number of times they will meet = n+1 = 13.

When they are moving towards each other , the situation will be same if they revolve around the circular path. But they will always have their directions opp to each other. So we must add their speeds.

Bunnel pls suggest a solution if the above is wrong.
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Re: How many times Swimmers meet? [#permalink]  06 Mar 2011, 13:00
the wording is poor, becuase it must state that they have to meet face to face.

The comment about the fact that they can also meet each other when faster swimmer overpasses lower swimmer would be relevant is there were other answer choices more than 13, but only A is the maximum number and seems to have logical solution.
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Re: How many times Swimmers meet? [#permalink]  06 Mar 2011, 19:41
I got 13.something

The swimmers will meet twice in (89/72 * 2) min or 89/36 mins. And the time lost by the slower swimmer will be recouped by the faster swimmer.

No of times they meet = 33 / (89 /36) = 33 * 36 / 89 = 13.x
Hence A
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Re: How many times Swimmers meet? [#permalink]  07 Mar 2011, 00:30
They will meet after every "c" minutes after the first meeting point. Why so?

They both will have to cover a distance = 89*2 = 178 ft to meet each other
And their relative speed will be: 53+19=72 ft/min

T=178/72=2.5(Approx). So, they meet after every 2.5 minutes after the first meeting point.

2.5*12=30 min; Thus they met at least 12 times.

Let's see how long it took for them to meet initially;

89/72 = 1.2 min(approx)

Thus; they have met 13 times in 30+1.2= 31.2 min approx.

To meet 14th time; they need extra 2.5 mins i.e. 31.2+2.5 = 33.7 minutes, which is more than 33 minutes.

Ans: "A"
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Re: How many times Swimmers meet?   [#permalink] 07 Mar 2011, 00:30
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