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You can put this solution on YOUR website!
\n" ); document.write( "Two tutors used similar methods to find an answer of 10.5 hours for the faster pipe to empty the tank working alone.
\n" ); document.write( "Then another tutor rightly pointed out that the answer of 10.5 hours can only be obtained by using the incorrect everyday interpretation of the phrase \"2.5 times faster\".
\n" ); document.write( "In sloppy everyday usage, \"2.5 times FASTER THAN\" is used to mean the same thing as \"2.5 times AS FAST AS\". But the two mean different things.
\n" ); document.write( "If x is the rate at which the slower pipe drains the pool, then if the faster pipe works 2.5 times AS FAST, then its rate of work is 2.5x.
\n" ); document.write( "But if the faster pipe works 2.5 times FASTER THAN the slower pipe, then its rate of work is x + 2.5x = 3.5x.
\n" ); document.write( "So, while the solution methods shown by the two tutors who got an answer of 10.5 hours are valid, they are not correct solutions to the problem as stated.
\n" ); document.write( "I will first show a very different method for getting the answer of 10.5 hours using the incorrect interpretation of the information given in the problem; then I will modify the answer using the correct interpretation.
\n" ); document.write( "Again let x be the rate at which the slower pipe drains the pool. If we use the interpretation that the faster pipe works 2.5 times AS FAST, then its rate is 2.5x.
\n" ); document.write( "The ratio of the two rates is x:2.5x, or 2x:5x, or 2:5.
\n" ); document.write( "That ratio means that, when the two pipes are working together, the slower pipe does 2/7 of the job and the faster pipe does 5/7 of the job.
\n" ); document.write( "Since the faster pipe does 5/7 of the job when working with the slower pipe, the time required for the faster pipe to drain the pool working alone will be 7/5 of the time required when the two are working together.
\n" ); document.write( "The problem tells us that the two pipes together take 7.5 hours; so the time required by the faster pipe alone would be 7/5 of 7.5 hours:
\n" ); document.write( "
\n" ); document.write( "The faster pipe alone would take 10.5 hours to drain the pool alone.
\n" ); document.write( "But, again, that is the answer to the wrong problem....
\n" ); document.write( "The actual rates are x and 3.5x; the faster drain does 7/9 of the total job; the time required for the faster tank to drain the pool alone using the correct interpretation of the given information is
\n" ); document.write( "
\n" ); document.write( "The correct answer to the problem as given is 135/14 hours. \n" ); document.write( "