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