GMAT Math

A museum offers four video programs that run continuously throughout the
day, each program starting anew as soon as it is finished. The first program
runs every 15 minutes, the second every 30 minutes, the third every 45
minutes, and the fourth every 40 minutes; the first show of each program
starts at 10:00 A.M. and the last showing of each program ends at 4:00 P.M.
If a tour group can watch the programs in any order, but needs at least ten
minutes between programs to regroup, what is the least amount of time
the group can take to watch all four programs?

CAN'T UNDERSTAND THE ANSWER

The first program plays every hour, hour: 15, hour:30, and
hour:45; the second plays every hour and half-hour; the third plays at 10:00, 10:45, 11:30, 12:15, and so
on; the fourth plays at 10:00, 10:40, 11:20, and so on. A look at this list shows that only the fourth show
is separated from any of the others by exactly 10 minutes. Thus, the fourth show should be viewed second
or third (i.e., somewhere in the middle) and at one of the times that does not start or end on the hour, so
that it is flanked by 2 waiting times of exactly 10 minutes each. The third waiting time must be at least 15
minutes, so the total time is at least the cumulative length of all four shows plus 35 minutes in waiting
time, or 165 minutes. (One sample schedule that achieves this minimum: 30-minute show 10:00--10:30,
40-minute show 10:40-11:20, 45-minute show 11:30-12:15, 15-minute show 12:30-12:45.)

It's probably easiest if you make a table, something like

first program: 10:00, 10:15, 10:30, ...
second program: 10:00, 10:30, 11:00, ...
third program: 10:00, 10:45, 11:30, ...
fourth program: 10:00, 10:40, 11:20, ...

then navigate the table, trying to minimize wait times.

For instance:

Watch the first video from 10:15 to 10:30. Take a ten minute break.
Watch the fourth video from 10:40 to 11:20. Take a ten minute break.
Watch the second video from 11:30 to 12:00. Take a ten minute break.
Wait 5 more minutes, then watch the second video from 12:15 to 1:00. Go home.

That gives us 35 minutes of wait time (3*10 + 1*5) plus the run time of the movies themselves.