For a project, A works for a few days and then B continues to do it. C comes to help when the project is half completed, and leaves when the project is completed (5/6). As a result, the task is completed exactly as planned, and B has done the total amount of the project If C does not come to help, and B only takes over A and continues to do it, it will be completed (10/3) days later than planned; if A alone does it all, it will be completed 6 days earlier than planned. It is known that the working efficiency of B is 3 times that of C. Question: How many days was the original planned construction period?
一项工程，甲先做若干天后由乙继续做，丙在工程完成一半时前来帮忙，待工程完成(5/6)时离去，结果恰好按计划完成任务，其中乙做了工程总量的一半；如果丙不来帮忙，仅由乙接替甲一直做下去，就会比计划推迟(10/3)天完成；如果全由甲单独做，就会比计划提前6天完成．已知乙的工作效率是丙的3倍．请问：原计划工期是多少天？
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">5 / 6</gadget>
<output>5/6 = around 0.833333</output>

<gadget id="calculator">(5/6) - (1/2)</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">(1/3) / 4</gadget>
<output>1/12 = around 0.083333</output>

<gadget id="calculator">(1/2) / (1/12)</gadget>
<output>6</output>

<gadget id="calculator">10 / 3</gadget>
<output>10/3 = around 3.333333</output>

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

<gadget id="calculator">20 - 6</gadget>
<output>14</output>

<gadget id="calculator">(1/2) + (1/12)</gadget>
<output>7/12 = around 0.583333</output>

<gadget id="calculator">14 / (7/12)</gadget>
<output>24</output>

<gadget id="calculator">24 + 6</gadget>
<output>30</output>

<result>30</result>