Answer:
The next two times that both buckets dump water at the same time are 5:12 P.M. and 7:04 P.M.
Step-by-step explanation:
To find out the next two times both buckets dump water at the same time we first must find the least common multiple (LCM) between the period it takes for each bucked to dump water, that is, LCM (14,16).
The numbers can be decomposed as 2 x 7 and 2 x 8, therefore, the LCM is:
[tex]LCM(14,16) = 2*7*8=112[/tex]
Since the last time that both buckets dumped water at the same time was 3:20 P.M., to discover when they will simultaneously dump water again we should add 112 minutes(1 h 12min) to the last time it happened:
[tex]T_{1}= 3:20 + 1:52 = 5:12 PM[/tex]
The same can be done to find next time that it will happen again:
[tex]T_{2}= 5:12 + 1:52 = 7:04 PM[/tex]
The next two times that both buckets dump water at the same time are 5:12 P.M. and 7:04 P.M.
