To fill a pool with water, if valves ①, ②, and ③ are opened at the same time, it can be completed in 7.5 hours; if valves ①, ③, and ⑤ are opened at the same time, it can be completed in 5 hours; if valves ①, ③, and ④ are opened at the same time, it can be completed in 6 hours ; If valves ②④⑤ are opened at the same time, it can be completed in 4 hours. Ask how many hours it will take to fill the pool if these five valves are opened at the same time.
放满一个水池的水，如果同时开放①、②、③号阀门，7.5小时可以完成；如果同时开放①、③、⑤号阀门，5小时可以完成；如果同时开放①③④号阀门，6小时可以完成；如果同时开放②④⑤号阀门，4小时可以完成．问同时开放这五个阀门，多少小时可以放满这个水池．
<gadget id="calculator">1 / 7.5</gadget>
<output>0.133333</output>

<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">(1/6) - (1/4)</gadget>
<output>-1/12 = around -0.083333</output>

<gadget id="calculator">0.133333 + (1/5) + (-1/12)</gadget>
<output>0.25</output>

<gadget id="calculator">0.25 / 3</gadget>
<output>0.083333</output>

<gadget id="calculator">0.083333 + (1/4)</gadget>
<output>0.333333</output>

<gadget id="calculator">1 / 0.333333</gadget>
<output>3.000003</output>

<result>3.000003</result>