For a job, it takes 10 days for A and B to cooperate, 12 days for B and C to cooperate, and 15 days for C and D to cooperate. How many days does it take for A and D to cooperate?
一件工作，甲乙合作要10天，乙丙合作要12天，丙丁合作要15天，请问甲丁合作需要多少天？
<gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>

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

<gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>

<gadget id="calculator">(1/15) - (1/12)</gadget>
<output>-1/60 = around -0.016667</output>

<gadget id="calculator">(1/10) + (-1/60)</gadget>
<output>1/12 = around 0.083333</output>

<gadget id="calculator">1 / (1/12)</gadget>
<output>12</output>

<result>12</result>