A bicycle tire, if it is installed on the front wheel, it will be discarded after driving 3000 kilometers; if it is installed on the rear wheel, it will be discarded after driving 5000 kilometers. According to this calculation, now buy a pair of such new tires and install them. In order to travel as much as possible, the method of changing the front and rear tires after the bicycle has traveled a certain distance is adopted. So how many kilometers can this pair of tires travel at most to be scrapped?
一种自行车轮胎，若安装在前轮上行驶3000千米后要报废，若安装在后轮上行驶5000千米后要报废．照这样计算，现在买来一对这样的新轮胎装上，为了行驶尽可能多的路，采用当自行车行驶一定路程后将前后轮胎调换的方法．那么这对轮胎最多可行驶多少千米要报废？
<gadget id="calculator">1 + 1</gadget>
<output>2</output>

<gadget id="calculator">1 / 5_000</gadget>
<output>1/5_000 = around 0.0002</output>

<gadget id="calculator">1 / 3_000</gadget>
<output>1/3_000 = around 0.000333</output>

<gadget id="calculator">(1/5_000) + (1/3_000)</gadget>
<output>1/1_875 = around 0.000533</output>

<gadget id="calculator">2 / (1/1_875)</gadget>
<output>3_750</output>

<result>3_750</result>