A, B, and C are three people. A walks 100 meters per minute, B walks 80 meters per minute, and C walks 75 meters per minute. A starts from the East Village, and B and C start from the West Village at the same time and walk toward each other. On the way, A meets B and then meets C after 3 minutes. Find the distance between the east and west villages.
甲、乙、丙三人，甲每分走100米，乙每分走80米，丙每分走75米，甲从东村，乙、丙从西村同时出发相向而行．途中甲与乙相遇后3分又与丙相遇，求东西两村的距离．
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">100 + 75</gadget>
<output>175</output>

<gadget id="calculator">1 / 175</gadget>
<output>1/175 = around 0.005714</output>

<gadget id="calculator">100 + 80</gadget>
<output>180</output>

<gadget id="calculator">1 / 180</gadget>
<output>1/180 = around 0.005556</output>

<gadget id="calculator">(1/175) - (1/180)</gadget>
<output>1/6_300 = around 0.000159</output>

<gadget id="calculator">(1/3) / (1/6_300)</gadget>
<output>2_100</output>

<result>2_100</result>