<PRE><B>Question 1121249</B>
&lt;br&gt;
Two tutors used similar methods to find an answer of 10.5 hours for the faster pipe to empty the tank working alone.&lt;br&gt;
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 &quot;2.5 times faster&quot;.&lt;br&gt;
In sloppy everyday usage, &quot;2.5 times FASTER THAN&quot; is used to mean the same thing as &quot;2.5 times AS FAST AS&quot;.  But the two mean different things.&lt;br&gt;
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.&lt;br&gt;
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.&lt;br&gt;
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.&lt;br&gt;
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.&lt;br&gt;
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.&lt;br&gt;
The ratio of the two rates is x:2.5x, or 2x:5x, or 2:5.&lt;br&gt;
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.&lt;br&gt;
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.&lt;br&gt;
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:&lt;br&gt;
{{{(7/5)*7.5 = (7/5)(15/2) = 21/2 = 10.5}}}&lt;br&gt;
The faster pipe alone would take 10.5 hours to drain the pool alone.&lt;br&gt;
But, again, that is the answer to the wrong problem....&lt;br&gt;
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&lt;br&gt;
{{{(9/7)*7.5 = (9/7)(15/2) = 135/14}}}&lt;br&gt;
The correct answer to the problem as given is 135/14 hours.</PRE>