There is a project that is done by three engineering teams in turn every day. The original plan was done in the order of A, B, and C, and it happened to be completed in one day; if it was done in turn in the order of B, C, and A, it would take 0.5 days more than the original plan; if it was done in turn in the order of C, A, and B, it would take more time than the original plan 1/3 days. It is known that A alone takes 13 days to complete the project, and the efficiency of the three engineering teams is different, so how many days will it take for this project to be completed by the three teams of A, B, and C?
有一项工程，由三个工程队每天轮流做．原计划按甲、乙、丙次序轮做，恰好整天完工；如果按乙、丙、甲次序轮流做，比原计划多用0.5天；如果按丙、甲、乙次序轮流做，比原计划多用1/3天．已知甲单独做13天完工，且3个工程队的效率各不相同，那么这项工程由甲、乙、丙三个队合作要几天？
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">1 + (1/2) + (3/4)</gadget>
<output>9/4 = around 2.25</output>

<gadget id="calculator">13 / (9/4)</gadget>
<output>52/9 = around 5.777778</output>

<result>52/9 = around 5.777778</result>