sunrat Posted January 2, 2014 Share Posted January 2, 2014 A tank has three taps. The first can fill the tank in 4 hours, the second can fill the tank in 2 hours and the third can empty the tank in 8 hours. How long will it take to fill the tank with all three taps operating at the same time? (You can assume the tank is empty to begin with). Quote Link to comment Share on other sites More sharing options...
Towncarman Posted January 2, 2014 Share Posted January 2, 2014 Quote Link to comment Share on other sites More sharing options...
sunrat Posted January 2, 2014 Author Share Posted January 2, 2014 Incorrect. Quote Link to comment Share on other sites More sharing options...
ross549 Posted January 2, 2014 Share Posted January 2, 2014 The math I did in my head seems to indicate an answer of 12. Quote Link to comment Share on other sites More sharing options...
Guest LilBambi Posted January 2, 2014 Share Posted January 2, 2014 (edited) 1.1 hours? Edited January 3, 2014 by LilBambi modified answer ... slipped a digit? Quote Link to comment Share on other sites More sharing options...
crp Posted January 2, 2014 Share Posted January 2, 2014 oh come on people, forget the math just use common sense. If the fastest tap can do it in 2 how can it possibly take longer than 2 if it is being helped out in filling the tank? Quote Link to comment Share on other sites More sharing options...
crp Posted January 2, 2014 Share Posted January 2, 2014 my quick guess: 1.142857142857143 hours Quote Link to comment Share on other sites More sharing options...
ross549 Posted January 2, 2014 Share Posted January 2, 2014 Pi? Adam Quote Link to comment Share on other sites More sharing options...
sunrat Posted January 2, 2014 Author Share Posted January 2, 2014 Still no correct answer. I'll give it a bit longer. Took me about 3 mins, 2 1/2 to work out a method and 30 sec to calculate. I ended up using a different method from where I sourced the puzzle but got the same answer. Quote Link to comment Share on other sites More sharing options...
zlim Posted January 3, 2014 Share Posted January 3, 2014 The math teacher in me comes out. In one hour the first tap will be able to fill 1/4 of the tank. The second tap will be able to fill 1/2 of the tank and meanwhile the third tap will remove 1/8 of the tanks contents. So 1/4 + 1/2 - 1/8 using a common denominator of 8 becomes 2/8 + 4/8 - 1/8 equals 5/8. In one hour 5/8 of the tank is filled. Let's see what happens if the taps operate for 2 hours. The first tap could fill 2/4, the second 2/2 while the third tap removes 2/8 of the contents. 2/4 + 1 - 1/4 means the tank overflows before it reaches the 2 hour mark. The correct answer is between 1 and 2 hours. To figure out the exact time I set up an equation like this 1/4x + 1/2x - 1/8x (where x presents time) and set it equal to 1 (which represents a full tank). Common denominator 2/8x +4/8x - 1/8x = 1 or 5/8x = 1. Who can solve for x? (I know I know, zlim wildly waves her hand). I'll let you figure it out and then sunrat can congratulate you on your correct answer. Quote Link to comment Share on other sites More sharing options...
réjean Posted January 3, 2014 Share Posted January 3, 2014 (edited) This is my final edit. Similar to zlim. In 2 hours the tank will be 1/2 + 1 - 1/4 full or 1 and 1/4 full. 2 hours being 120 min. It will take 96 min to fill it up. Edited January 3, 2014 by réjean Quote Link to comment Share on other sites More sharing options...
sunrat Posted January 3, 2014 Author Share Posted January 3, 2014 zlim, yes. rejean, sorry no. Edit - your edited post is correct. Quote Link to comment Share on other sites More sharing options...
Webb Posted January 3, 2014 Share Posted January 3, 2014 I came up with the same formula as zlim but I reduced the fractions before adding them. One hour = 2/8 + 4/8 - 1/8 = 5/8. It's been too long since math so I don't know what 5/8x=1 means and I would probably start using trial and error. If one hour = 5/8 then 2 hours = 10/8 so it's less than 2 hours but I'm lost after that. I'll bet I could figure it out when I was in jr. high. Quote Link to comment Share on other sites More sharing options...
crp Posted January 3, 2014 Share Posted January 3, 2014 I came up with the same formula as zlim but I reduced the fractions before adding them. One hour = 2/8 + 4/8 - 1/8 = 5/8. It's been too long since math so I don't know what 5/8x=1 means and I would probably start using trial and error. If one hour = 5/8 then 2 hours = 10/8 so it's less than 2 hours but I'm lost after that. I'll bet I could figure it out when I was in jr. high. oh, if you don't remember how to do it, just use the computers of the internet. i checked my answer against http://www.wolframalpha.com/input/?i=5%2f8x%3d1&incTime=true , reason i checked is because sunrat wrote rejean was wrong. Quote Link to comment Share on other sites More sharing options...
sunrat Posted January 3, 2014 Author Share Posted January 3, 2014 You're on the right track. If 1 hr = 5/8x then x=8/5 hrs or 1.6 hrs ie, 1hr 36mins. rejean's edited answer is correct, but it wasn't edited when I read it before my last post. I actually worked it out by assuming the tank was a common multiple size of 16 litres, then it would fill at 8+4-2=10 l/hr, so 1.6 hrs. Less mathematical but more practical. This puzzle was brought to you by Pzzlr, where they post a new puzzle every few days. Some are wickedly hard. Quote Link to comment Share on other sites More sharing options...
réjean Posted January 3, 2014 Share Posted January 3, 2014 feeling better. Quote Link to comment Share on other sites More sharing options...
Guest LilBambi Posted January 3, 2014 Share Posted January 3, 2014 Excellent puzzle! Thanks sunrst! Great fun! Quote Link to comment Share on other sites More sharing options...
abarbarian Posted January 4, 2014 Share Posted January 4, 2014 Some are wickedly hard. An this one was not ? Quote Link to comment Share on other sites More sharing options...
sunrat Posted January 5, 2014 Author Share Posted January 5, 2014 An this one was not ? This one was comparatively easy. Quote Link to comment Share on other sites More sharing options...
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