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algebra 2 word problem

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Let assume that speed of beetle K is sk and it ran 30/sk seconds. Then beetle J start running with speed 3sk and ran 90/(3sk) seconds. Because we know, that the total time of the relay is 40 seconds, we can write the equation:
30/sk+90/(3sk)=40 ---> 30/sk+30/sk=40 ---> 60/sk=40 ---> sk=60/40
              ↓       
             30/sk  

So, the speed (rate) of beetle K is 1.5 cm/sec
                                  beetle J is 4.5 cm/sec.