It takes 10 days for teams A, B, and C to complete a project together. It is known that the work efficiency of A is 3 times that of C, and the work efficiency of B is 2 times that of C. During the construction process, Team A rests for 4 days, and Team B rests for 9 days. The two teams cannot rest at the same time, and Team C does not rest. So how many days did the three teams work together?
甲、乙、丙三队共同完成一项工程需要10天．已知甲的工作效率是丙的3倍，乙的工作效率是丙的2倍．施工过程中，甲队休息4天，乙队休息9天，甲乙两队不能同时休息，丙队没有休息．那么三队一起工作的天数是多少？
<gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>

<gadget id="calculator">3 + 2 + 1</gadget>
<output>6</output>

<gadget id="calculator">2 / 6</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">(1/10) * (1/3)</gadget>
<output>1/30 = around 0.033333</output>

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

<gadget id="calculator">(1/10) * (1/6)</gadget>
<output>1/60 = around 0.016667</output>

<gadget id="calculator">(1/30) + (1/60)</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">(1/20) * 4</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">3 / 6</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">(1/10) * (1/2)</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">(1/20) + (1/60)</gadget>
<output>1/15 = around 0.066667</output>

<gadget id="calculator">(1/15) * 9</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">1 - (1/5) - (3/5)</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">(1/5) / (1/10)</gadget>
<output>2</output>

<result>2</result>