Music/Math Word Problem

Question

If you play a song at 118 beats per minute, it takes 4 minutes, 35 seconds to play. If you slow the tempo down to 100 beats per minute, how long does it take to play this song? Answer in terms of minutes and seconds, rounding to the nearest second.

Answer 1

This problem has a ton of proportions in it. Usually, when you see the word "per," you should expect division or proportions.

 

 

First, let's figure out how many beats the song has. At 118 beats per minute, it takes 4 minutes and 35 seconds to play the song. Change minutes and seconds into minutes:

 

4 minutes and 35 seconds = 4 and 35/60 minutes = 4 and 7/12 minutes = 55/12 minutes

 

 

Now set up a proportion to figure out how many beats there are in the song:

 

118 beats / 1 minute = x beats / (55/12) minutes

118(55/12) = x

540.8333 = x

 

The song has around 540.8333 beats.

 

 

Now set up a proportion for the slower tempo:

 

100 beats / 1 minute = 540.8333 beats / x minutes

100x = 540.8333

x = 5.4083

 

 

It will take 5.4083 minutes to play the song at the slower tempo. But the problem asks for an answer in minutes and seconds, so let's convert that back with another proportion:

 

60 seconds / 1 minutes = x seconds / 0.4083 minutes

24 = x

 

 

It will take 5 minutes and 24 seconds to play the song.