Question

An indoor water park has two giant buckets that slowly fill with 1000 gallons of water before dumping it on the people below. One bucket dumps water every 16 minutes. The other bucket dumps water every 14 minutes. It is currently 3:25 P.M. and both buckets dumped water 5 minutes ago. Find the next two times that both buckets dump water at the same time.
First time: P.M

Answer 1

16 min bucket will drop at 3:36 and 14 min bucket will drop at 3:31

Answer 2

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:

$LCM(14,16) = 2*7*8=112$

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:

$T_{1}= 3:20 + 1:52 = 5:12 PM$

The same can be done to find next time that it will happen  again:

$T_{2}= 5:12 + 1:52 = 7:04 PM$

The next two times that both buckets dump water at the same time are 5:12 P.M. and 7:04 P.M.