College

The high school dance team is learning a new routine to a song that lasts 3 minutes and 41 seconds, or 221 seconds in total. Yesterday, they covered the first 45 seconds of the song at practice. They learn an average of 22 seconds of the dance in an hour. Let [tex]$h$[/tex] represent the time, in hours, it will take the team to learn the entire dance.

Which equation represents this situation, and how long will it take?

A. [tex]$221 = 45 + 22h$[/tex]; 5 hours

B. [tex]$221 = 22h$[/tex]; 11 hours

C. [tex]$221 = 22h - 45$[/tex]; 12 hours

D. [tex]$221 = 22h + 45$[/tex]; 8 hours

Answer :

To solve the problem, let's break it down:

1. Total Duration of the Song:
The song lasts 221 seconds.

2. Duration Already Covered:
The dance team has already learned the first 45 seconds of the song.

3. Time Remaining to Be Learned:
To find out how much more they need to learn, subtract the seconds they have already covered:
[tex]\[
\text{Remaining seconds to learn} = 221 - 45 = 176 \text{ seconds}
\][/tex]

4. Learning Rate:
The team learns an average of 22 seconds of the dance per hour.

5. Determine the Time Needed (in hours):
To find how long it will take to learn the remaining 176 seconds, divide the remaining seconds by the rate at which the team learns:
[tex]\[
h = \frac{176}{22} = 8 \text{ hours}
\][/tex]

6. Equation Representation:
To put this into an equation form, the scenario is that they need to learn a total of 221 seconds, with 45 learned, and at a rate of 22 seconds per hour. So, the equation can be set up as:
[tex]\[
221 = 22h + 45
\][/tex]
Solving for [tex]\( h \)[/tex] should give us the value of 8 hours, which aligns with our calculation.

From the options provided, the correct choice is:
- D. [tex]\( 221 = 22h + 45; 8 \)[/tex] hours.

Therefore, it will take the dance team 8 hours to learn the entire dance routine.