Question

Alice, Beth, and Cynthia start running

laps together around a track at 7 A.M. They
begin running at the starting line. It
takes Alice 15 seconds to complete lap.
It takes Beth 20 seconds to complete lap,
and it takes Cynthia 30 seconds to
complete lap. Suppose the runners
continue at these rates. At what time will
all three runners next meet again at the
starting line?

Answer 1

To find when three runners will meet at the starting line again, calculate the LCM of their lap times. In this case, the LCM of 15, 20, and 30 seconds is 60 seconds, so they will meet after 1 minute at 7:01 A.M.

Step-by-step explanation:

The question involves finding the time when three runners will all meet at the starting line after starting to run from the same point at different speeds. To solve this, we need to calculate the Least Common Multiple (LCM) of their lap times. Alice completes a lap in 15 seconds, Beth in 20 seconds, and Cynthia in 30 seconds. The LCM of 15, 20, and 30 is 60 seconds. Therefore, all three runners will meet at the starting line again after 60 seconds of running.

Since they begin running at 7 A.M., we add 60 seconds (which is 1 minute) to this start time. Hence, they will all meet at the starting line at 7:01 A.M.