algebra 2 word problem

Question

iIn a total time of 40 seconds, beetle K ran in a straight line for 30 cm and bumped into beetle J, (at this point beeltee K stopped) then beetle J ran for another 90 cm at 3 times the rate of beetle K. What was the rate of each beetle?

Answer 1

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

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