Math Help

<p>One pipe can fill a pool 1.25 times faster than a second pipe. When both pipes are opened, they fill the pool in five hours. How long would it take to fill the pool if only the slower pipe is used?</p>

<p>Making up numbers again (my favorite method):</p>

<p>Suppose the slow pipe fills at 4 gallons per hour. Then the fast pipe is 1.25 x faster so that’s 5 gallons per hour. Together: 9 gallons per hour, which they do for 5 hours, so the tank holds 9 x 5 = 45 gallons. So working alone, the slow one takes 45/4 = 11.25 hours.</p>

<p>But where does this problem come from? The reason that I ask is that I am bothered by the phrase “1.25 times FASTER”. I am assuming that they meant “1.25 times as fast”. But it is an ambiguous wording.</p>

<p>One pipe can fill a pool 1.25 times faster than a second pipe. When both pipes are opened, they fill the pool in five hours. How long would it take to fill the pool if only the slower pipe is used?</p>

<p>rate of pipe 1(fast): x
rate of pipe 2(slow): 1.25x
together: 5</p>

<p>rate of pipe 1 per hour: 1/x
rate of pipe 2 per hour: 1/1.25x
together: 1/5</p>

<p>5x(1/x+1/1.25= 1/5)
5+4= x
9=x</p>

<p>1.25x= 9(1.25)= 11.25</p>

<p>Here is how I approached the problem</p>

<p>Slower=1
Faster=1.25
Together= 1+ 1.25= 2.25</p>

<p>2.25 : 5
1 : x</p>

<p>Indirect proportion: (2.25 x 5)/1 = x</p>

<p>time to solve: ~7 seconds</p>

<p>I like the plug in method too; I probably would have used that if I had thought of it first :P</p>