A radio station dedicates 20% of their air time to commercials for each radio show. During a radio show, 30 minutes of commercials played. How long was the radio show?

150 minutes (2.5 hours)

Step-by-step explanation:

We must consider that the total time that the radio program lasted represents the 100%.

Of that 100% we are told that 20% is dedicated to commercials. So the 30 minutes of commercials correspond to 20% of the air time, which can be represented in the following table:

Percentage of time time

20% ⇒ 30min

and we are looking for how long the show was on the air (the 100%).

So updating the table (I will call x the total time on the air):

Percentage of time time

20% ⇒ 30min

100% ⇒ x

This reationship between three values can be solve by the rule of three: multiply the cross quantities on the table (100 by 30) and divide by the remaining amount (20):

x = 100*30 / 20

x = 3000 / 20

x = 150 minutes

The radio show was 150 minutes (2.5 hours) long.