A cat and a mouse move in opposite directions at the same point on a circle with a diameter of 100 meters. A cat walks 18.84 meters per minute, and a mouse walks 12.56 meters per minute. When the cat and the mouse met for the first time, by how many meters did the cat walk farther than the mouse?
猫和老鼠在一个直径是100米的圆周上的同一个地点向相反方向运动．猫每分钟走18.84米，老鼠每分钟走12.56米．当猫和老鼠第一次相遇时，猫比老鼠多走了多少米？
<gadget id="calculator">100 / 2</gadget>
<output>50</output>

<gadget id="calculator">50 ** 2</gadget>
<output>2_500</output>

<gadget id="calculator">18.84 + 12.56</gadget>
<output>31.4</output>

<gadget id="calculator">2_500 / 31.4</gadget>
<output>79.617834</output>

<gadget id="calculator">18.84 - 12.56</gadget>
<output>6.28</output>

<gadget id="calculator">3.14 * 79.617834 * 6.28</gadget>
<output>1_569.999992</output>

<result>1_569.999992</result>