batch of parts is completed in 12 hours by A, 15 hours by B, and 20 hours by C. Now this batch of parts is equally distributed to A and B for processing. C first helped A to do it for a while, and then helped B to do it until it was finished. At this time, A and C finished the work at the same time. How long did A work?
一批零件，甲12小时完成，乙15小时完成，丙20小时完成，现在把这批零件平均分给甲、乙加工．丙先帮甲做了一会儿，然后又帮乙做，直至完成，这时甲、丙恰好同时完工，甲做了几小时？
<gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>

<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>

<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">(1/12) + (1/15) + (1/20)</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">1 / (1/5)</gadget>
<output>5</output>

<result>5</result>