How many minutes did nick play in the hockey game?

Question

During a hockey game brandon played 7 less minutes than nick. zach played 12 more minutes than brandon, hunter played twice as long as zach. Hunter played for 44 minutes. how many minutes did nick play in the hockey game?  Please show work..

Answer 1

Hi, Sasha

Lets start this problem setting up the different equations and identifying each variable.

 

Let b be the # of minutes that Brian played.

Let z be the # of minutes that Zachary played.

Let b be the # of minutes that Hunter played.

 

Now,  I am going to translate each relevant piece of information that the problem gives me into algebra. Let the fun begin :)

 

1) Brian played 7 minutes less than Nick

b= n -17

 

2) Zachary played 12 minutes more than Brandon

z= b+ 12

 

3) Hunter played twice as long as Zachary. 

h= 2z

 

4) Hunter played 44 minutes.  

 

I am work this problem starting with the last piece of information, that Hunter played twice as long as Zachary.  If Hunter played 44 min., that means that Zachary must have played 22 min. Look at equation #3. 

h= 2z   If you divide both sides by 2.  You have z= h/2 or 44/2= 22

 

Next, I am going to use equation # 2 to ascertain how long Brian played.  We are told that Zachary played 12 minutes longer than Brian. Since Zachary played 22 minutes, this means that Brian played for 10 minutes. This is how.  Using the second equation and substituting for Z.

22 = b+ 12, subtract 12 from both sides. b= 10, so Brian played for 10 minutes.

 

Are you dizzy yet!? Don't despair, we are almost don't :)

 

Now that we know that Brian played for 10 minutes.  We can figure out how long Nick played by using equation #1. I am going to substitute 10 for b.

 

10= n-17 , adding 17 to both sides

27=n

So, big Nick played for 27 minutes...hey, I am assuming he is tall... after all he plays basket played.  Well... it was a long problem..

 

Good luck

 

D.Y. Taylor

Answer 2

When looking at word problems, we might want to start by translating the english into math.

 

So, here is the original paragraph:

 

During a hockey game brandon played 7 less minutes than nick. zach played 12 more minutes than brandon, hunter played twice as long as zach. Hunter played for 44 minutes.

 

Here is the first step of the "math" translation. Let's use initials for names:

B played 7 less minutes than N. Z played 12 more minutes than B, H played twice as long as Z. H played for 44 minutes.

 

Now I will substitute "=" for "played" and drop the "minutes".

B = 7 less than N. Z = 12 more than B, H = twice Z. H =44.

 

Finally, words like "less than" and "more than" and "twice":

B = N-7. Z = 12+B, H = 2Z. H =44.

 

I hope you see the four equations and working backwards from H=44 you can now figure out Z, B, and N.