Quick
Answer:
Nine more
shows. 

Complete
Solution:
You can consider
this problem in terms of minutes or in units of halfhour
shows. Using only the SP setting, the tape
can record 120 minutes of shows. If one 30 minute show
has already been recorded, 1/4 of the tape has been used.
Type
of Setting 
Minutes
Used 
Total
Minutes on Tape 
Portion
of Tape Used 
SP 
30 
120 
30/120
or 1/4 
EP 
(1/4)
×
360, or 90 
360 
90/360
or 1/4 
With 1/4 of the tape filled, 90 minutes
of EP has been used, so that there are 36090 or 270 minutes
left. At 30 minutes per show, nine additional shows can
be taped.
If you are using
halfhour units, there are four halfhour shows
on SP in two hours. One halfhour show used 1/4 of the
tape. Threefourths of the tape is left. With EP, you
can do 12 halfhour shows, and then you have enough tape
for 3/4 ×
12, or 9 shows remaining.
Yet another way
to consider this problem is to use proportions
as follows:
Because 3 ×
120 = 360 and 3 ×
30 = 90, there are 90 minutes used on the EP setting,
so that there are 360  90, or 270 minutes available which
allows for 9 thirtyminute shows
on EP.
Similarly 30 ×
360 = 120 ×
(x number of minutes), so the number of minutes
is 90. 
