When will the two satellites meet again? (Date and time)

Question

One satellite makes one revolution around the earth every 20 hours, the other makes one revolution every 25 hours. At 8:00 a.m. On December 3 they were together. When will they meet again (date and time)?

Answer 1

The amount of time from 8:00 a.m. December 3 to the very next date/time when the satellites are together is evenly divisible by 20 hours and it is evenly divisible by 25 hours.

 

The LCM (Least Common Multiple) of 20 and 25 is 100.  We find the LCM by looking at the factors:

      Of 20:     2*2*5

      Of 25:     5*5

    And selecting the least value that includes the common factors (that is, 2*2*5*5 = 100)

 

So, in 100 hours, the satellites will be together again.

 

Now, when is that?

 

With 24 hours per day, that is:    100/24

                                                     = 4 1/6 days

                                                     = 4 days 4 hours

                      December 3 + 4 days = December 7

                            8:00 a.m. + 4 hours = noon

At 12:00 p.m.  (Noon) on December 7, the satellites will be together again.