A and B are training on a circular runway. They start from the same place at the same time and walk with their backs facing each other. After the two met, they immediately turned around and continued to move forward. At the beginning, A's speed was 160 meters per minute, and B's speed was 120 meters per minute. After the U-turn, A's speed increased by half, and B's speed increased by one-third. If the runway is 500 meters long, how far is the distance between the place where A and B meet for the first time and the place where they meet for the second time? (The distance between two points on the circular route refers to the shortest distance along the runway)
甲、乙两人在环形跑道上训练，他们从同一地点同时出发，背向而行．两人相遇后立即调头，继续前进，一开始甲的速度是每分钟160米，乙的速度是每分钟120米，调头后甲的速度提高了一半，乙的速度提高了三分之一．若跑道长500米，甲、乙两人第一次相遇地点与第二次相遇地点相距多远？(环形路线上两点的距离指沿跑道的最短距离)
<gadget id="calculator">160 + 120</gadget>
<output>280</output>

<gadget id="calculator">500 / 280</gadget>
<output>25/14 = around 1.785714</output>

<gadget id="calculator">(25/14) * 160</gadget>
<output>2_000/7 = around 285.714286</output>

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

<gadget id="calculator">1 + (1/2)</gadget>
<output>3/2 = around 1.5</output>

<gadget id="calculator">160 * (3/2)</gadget>
<output>240</output>

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

<gadget id="calculator">1 + (1/3)</gadget>
<output>4/3 = around 1.333333</output>

<gadget id="calculator">120 * (4/3)</gadget>
<output>160</output>

<gadget id="calculator">240 + 160</gadget>
<output>400</output>

<gadget id="calculator">500 / 400</gadget>
<output>5/4 = around 1.25</output>

<gadget id="calculator">(5/4) * 120</gadget>
<output>150</output>

<gadget id="calculator">(2_000/7) - 150</gadget>
<output>950/7 = around 135.714286</output>

<result>950/7 = around 135.714286</result>