Math Is Fun Forum

iamfriendly

Member

Registered: 2009-07-03

Posts: 72

pools and Time

So we were doing the Gauss Math Contest (no worries, Im not cheating, back home to have lunch). So the Last qustion was this:

In a garden, the gardener opens Tap A and Tap B to fill his pool with water. That took 6 hours. The length of time of one of the Tap fill the pool indivisually would be x. How many possibilities are x (now obviously it doen't matter if it's Tap A or B,)?

Choices a) 5       b) 6          C) 9            d) 10             e)12

This may seems very easy to many people out there., but if one of you can Help Me, I would really appreciate your help

P.S. I was able to come up with only 12hr&12hr for the taps, OH yeah, only "positive interger" hours (e.g. 3 hr, not 3 1/4 hrs)

Last edited by iamfriendly (2010-05-11 04:46:50)

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ZHero

Real Member

Registered: 2008-06-08

Posts: 1,889

Re: pools and Time

Its c) 9

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iamfriendly

Member

Registered: 2009-07-03

Posts: 72

Re: pools and Time

Why, Please explain, Thank you

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EYE AM FRIENDLY, THAT'S O U NEED 2 NO,
psst,
Don't trust strangers, EYE AM FRIENDLY, THAT'S O U NEED 2 NO ..........psst, Don't trust strangers......

ZHero

Real Member

Registered: 2008-06-08

Posts: 1,889

Re: pools and Time

Let the time taken by the second tap be y hrs (to fill the tank completely individually)...
In 1 hr, both the tanks will fill..
(1/x + 1/y)th of the total capacity of tank which should be 1/6.

1/x + 1/y = 1/6

6(x+y)=xy

xy-6x-6y=0

(x-6)(y-6)=36

(x-6)(y-6)=1×36=2×18=3×12=4×9=6×6

these factors will give you different values of x and y.

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If two or more thoughts intersect, there has to be a point!

iamfriendly

Member

Registered: 2009-07-03

Posts: 72

Re: pools and Time

But, wouldn't those be less than 6 Hrs?, A tap is helping the other tap, which is equal or less than 6hr, that's gotta be faster than 6 hr!!

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EYE AM FRIENDLY, THAT'S O U NEED 2 NO,
psst,
Don't trust strangers, EYE AM FRIENDLY, THAT'S O U NEED 2 NO ..........psst, Don't trust strangers......

ZHero

Real Member

Registered: 2008-06-08

Posts: 1,889

Re: pools and Time

Well... See..
Different possible values of x and corresponding values of y are..

x-6=1 ; y-6=36

x-6=2 ; y-6=18

x-6=3 ; y-6=12

x-6=4 ; y-6=9

x-6=6 ; y-6=12

also, x can take all those values which y can take and thus there are total 9 different values possible!

Note that in all the cases, the values of x or y (i.e. the time taken) is More than 6 hrs.
When they're open together, they fill it in 6 hrs which is less than both their individual times!

Your Welcome

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If two or more thoughts intersect, there has to be a point!

iamfriendly

Member

Registered: 2009-07-03

Posts: 72

Re: pools and Time

So it's 7&42, 8&24, 9&18, 10&15, 12&12 (typo i guess,  for x-6=6, y-6=12, should be =6), a total of 9 possibilities?

Last edited by iamfriendly (2010-05-11 08:38:22)

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EYE AM FRIENDLY, THAT'S O U NEED 2 NO,
psst,
Don't trust strangers, EYE AM FRIENDLY, THAT'S O U NEED 2 NO ..........psst, Don't trust strangers......

ZHero

Real Member

Registered: 2008-06-08

Posts: 1,889

Re: pools and Time

Yes! That's exactly what you're looking for!

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If two or more thoughts intersect, there has to be a point!

iamfriendly

Member

Registered: 2009-07-03

Posts: 72

Re: pools and Time

Thank you for your help.

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EYE AM FRIENDLY, THAT'S O U NEED 2 NO,
psst,
Don't trust strangers, EYE AM FRIENDLY, THAT'S O U NEED 2 NO ..........psst, Don't trust strangers......