A project will be completed in 20 days by A alone, 30 days by B alone, and 40 days by C alone. Now there are three people working together. A rests for a few days due to illness, so it took 12 days to complete the project. , How many days did A rest?
一项工程，甲独做要20天完成，乙独做要30天完成，丙独做要40天完成，现由三人合作，中间甲因病休息了几天，所以12天才完成这项工程，甲休息了几天？
<gadget id="calculator">1 / 30</gadget>
<output>1/30 = around 0.033333</output>

<gadget id="calculator">1 / 40</gadget>
<output>1/40 = around 0.025</output>

<gadget id="calculator">(1/30) + (1/40)</gadget>
<output>7/120 = around 0.058333</output>

<gadget id="calculator">(7/120) * 12</gadget>
<output>7/10 = around 0.7</output>

<gadget id="calculator">1 - (7/10)</gadget>
<output>3/10 = around 0.3</output>

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

<gadget id="calculator">(3/10) / (1/20)</gadget>
<output>6</output>

<gadget id="calculator">12 - 6</gadget>
<output>6</output>

<result>6</result>