There are two typists, A and B, but only one computer to type a manuscript. If A can type it, it can be completed in 10 hours. If B can type it, it will take 12 hours to complete it. Now the two take turns playing, each playing for half an hour each time. First, A plays for half an hour, and B rests; then B plays for half an hour, and A rests, and A continues to play for half an hour... So how much time will it take for A and B to finish typing this manuscript?
打一份稿件，有甲、乙两名打字员，但只有一台电脑，若让甲来打，10小时可以完成，若让乙来打，需要12小时完成．现在两人轮流打，每人每次打半小时．先由甲打半小时，乙休息；接着乙打半小时，甲休息，再由甲接着打半小时…，那么打完这份稿件甲、乙共需要多少时间？
<gadget id="calculator">10 / 1</gadget>
<output>10</output>

<gadget id="calculator">10 / 2</gadget>
<output>5</output>

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

<gadget id="calculator">12 / 2</gadget>
<output>6</output>

<gadget id="calculator">5 + 6</gadget>
<output>11</output>

<gadget id="calculator">11 / 120</gadget>
<output>11/120 = around 0.091667</output>

<gadget id="calculator">(11/120) * 10</gadget>
<output>11/12 = around 0.916667</output>

<gadget id="calculator">1 - (11/12)</gadget>
<output>1/12 = around 0.083333</output>

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

<gadget id="calculator">(1/12) - (1/20)</gadget>
<output>1/30 = around 0.033333</output>

<gadget id="calculator">(1/30) / (1/12)</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">10 + 0.5 + (2/5)</gadget>
<output>10.9</output>

<result>10.9</result>