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1 April, 01:42

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?

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  1. 1 April, 01:59
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    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.
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