A and B walk towards each other from two places 2000 meters apart at the same time. A walks 55 meters per minute, and B walks 45 meters per minute. If a dog and A walk in the same direction at the same time, 120 meters per minute, encounter After arriving at B, immediately turn around and run to A, and run to B again when meeting A. Keep going back and forth like this until A and B meet, how many meters has the dog traveled in total?
甲、乙两人同时从相距2000米的两地相向而行，甲每分钟行55米，乙每分钟行45米，如果一只狗与甲同时同向而行，每分钟行120米，遇到乙后，立即回头向甲跑去，遇到甲再向乙跑去．这样不断来回，直到甲和乙相遇为止，狗共行了多少米？
<gadget id="calculator">45 + 55</gadget>
<output>100</output>

<gadget id="calculator">2_000 / 100</gadget>
<output>20</output>

<gadget id="calculator">120 * 20</gadget>
<output>2_400</output>

<result>2_400</result>