The distance between A and B is 27 km. A and C walk from A to B, and B walks from B to A. A travels 4 kilometers per hour, B travels 3 kilometers per hour, and C travels 2 kilometers per hour. The three start at the same time, how many hours later does A just reach the midpoint of the distance between B and C? It is required to write the key problem-solving reasoning process.
A、B两地相距27千米．甲、丙两人从A地向B地行走，乙从B地向A地行走．甲每小时行4千米，乙每小时行3千米，丙每小时行2千米．三人同时出发，问几小时后甲刚好走到乙、丙两人距离的中点？要求写出关键的解题推理过程．
<gadget id="calculator">3 - 2</gadget>
<output>1</output>

<gadget id="calculator">4 + 4 + 1</gadget>
<output>9</output>

<gadget id="calculator">27 / 9</gadget>
<output>3</output>

<result>3</result>