There is a project that three engineering teams, A, B, C, take turns to complete every day, which happens to be completed in a whole number of days; if they are done in turn in the order of B, C, A, it will take (1/2) more days than the original plan; Use more (1/3) days. It is known that A, B, and C work together at the same time, and it takes (124/9) days to complete, and the effects of the three engineering teams are different. How many days will it take for A to complete this project alone?
有一项工程，甲乙丙3个工程队每天轮流做，恰好整数天完成；如果按乙丙甲次序轮流做，比原计划多用(1/2)天；如果按丙甲乙次序轮流做，比原计划多用(1/3)天．已知甲乙丙同时合做，需要(124/9)天完成，且3个工程队的功效各不相同．这项工程由甲单独做几天才能完工？
<gadget id="calculator">124 / 9</gadget>
<output>124/9 = around 13.777778</output>

<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">(124/9) * (9/4)</gadget>
<output>31</output>

<result>31</result>