Math  /  Numbers & Operations

Question104. A television station has 20 min of advertising each hour. How many 30 -second ( 12min\frac{1}{2}-\mathrm{min} ) commercials can be run in a. 1 hr b. 1 day

Studdy Solution

STEP 1

What is this asking? How many half-minute ads can fit into 20 minutes, and then how many can fit in a whole day? Watch out! Don't forget to convert the day into minutes correctly!

STEP 2

1. Commercials per hour
2. Commercials per day

STEP 3

Alright, so we have **20 minutes** of ad time every hour.
Each commercial is **half a minute** long.
To figure out how many commercials we can fit, we're going to divide the **total ad time** by the **length of each commercial**.
This is like figuring out how many half-minutes fit into 20 minutes!

STEP 4

20 minutes12 minute/commercial \frac{20 \text{ minutes}}{ \frac{1}{2} \text{ minute/commercial} }

STEP 5

Dividing by a fraction is the same as multiplying by its reciprocal.
The reciprocal of 12\frac{1}{2} is 21\frac{2}{1} or just **2**.
So, we multiply **20** by **2**:

STEP 6

202=40 commercials 20 \cdot 2 = \textbf{40 commercials}

STEP 7

So, we can fit **40** commercials in one hour!

STEP 8

Now, let's scale this up to a whole day.
There are **24 hours** in a day.
We already know we can fit **40 commercials** per hour.
To find the total number of commercials in a day, we multiply the **commercials per hour** by the **number of hours in a day**.

STEP 9

40commercialshour24 hours 40 \frac{\text{commercials}}{\text{hour}} \cdot 24 \text{ hours}

STEP 10

4024=960 commercials 40 \cdot 24 = \textbf{960 commercials}

STEP 11

Wow, that's a lot of commercials!
We can fit a whopping **960** commercials in a day!

STEP 12

a. **40** commercials can run in 1 hour. b. **960** commercials can run in 1 day.

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