It’s been a while since I’ve written about a mathematics problem from NCTM and I kinda of miss writing about them (You can read the other ones here and here)! Last week they posted a question that only got snarky answers on Facebook, so I decided this would be the perfect one to write about 🙂

Here’s the post:

From the snarky answers it seems to have drawn criticism because of the number of movies Ryan supposedly has, but I just have to say from my own experience that my children could certainly given Ryan a run for his money in the movie collection department!

Anyway, Ryan’s movie collection is apparently quite extensive. Also, he only likes movies that are fairly short (1 hour and 30 minutes in total). If Ryan were to watch these movies back to back to back to back to (you get it, all 70 without stopping); how many days would it take him to watch said movies?

Can you tell right off the bat that this is a conversion situation?

**My game plan:**

Convert hours and minutes to the same unit of measure; then use this unit of measure to calculate the number of days of the marathon movie watching!

Except that as I was typing this, I came up with another game plan . . . each pair of movies equals 3 hours. Then, I don’t have to worry about converting minutes to hours or hours to minutes. AND, 70 is an even number of movies, meaning I can make pairs of movies without leaving any movies out. AND, 3 hours is a really nice value to have when dealing with days, because there are 24 hours in a day and 3 divides 24 evenly. So, I can watch 8 pairs of movies a day (or 16 movies a day).

**New Game Plan:**

16 goes in to 70 little more than 4 times (actually it goes into 70, 4.375 times)

That means Ryan will need to watch 8 pairs of movies for 4 days. At the end of 4 days he will have watched 64 movies, leaving him the final 6 movies (or 3 pairs of movies, or 9 hours of movies) for the 5th day.

So my final answer is 4 days and 9 hours of movies to watch all 70 movies!

Just to double check, you could do the converting I described at the beginning of the post . . .OR you could describe a different method to do the calculations if the mood strikes you! If you do this another way, I’d love to hear about it in the comments below!

I also feel the need to address the posts on Facebook about Ryan’s movie situation. Most of the comments were along the lines of “only a mathematics website, textbook, teacher, etc., etc. would ask such a silly question. This question isn’t realistic.” I must say I have to respectfully disagree. The first thing I thought about when I read this question was the Brita water filter commercial showing plastic water bottles stretched across the Earth’s surface.

If this commercial had been written as a word problem in a mathematics class, it probably would have sounded a little something like this:

*The makers of Brita water filters claim that 1 filter is able to filter the equivalent of 300, 16.9 oz. bottles of water. Suppose Ryan uses 1 Brita water filter per month for one year. If Ryan had used plastic bottles, instead of water filters how many times could the number of plastic bottles used wrap around the equator of the Earth?*

I’m willing to admit that this type of problem situation isn’t one that we encounter in our every day lives; however these types of conversion situations come up whether they be for impact, or marketing, or something else. Isn’t nice to know that you . . . reader of the It’s Just Math Blog have a way to evaluate such statements for their accuracy?

And finally, with regard to Ryan and his movie watching I’m willing to bet that the following problem statement may have been a little more well-received. Why? You might ask? Because most of us know someone who’s done this 🙂 If this problem statement had been written about me it would have been about watching Law and Order SVU marathons 🙂

*Suppose Ryan is a huge fan of James Bond movies. In fact, this weekend he plans to watch every James Bond movie ever made back-to-back. Will he have enough time to watch all of the movies if he starts Saturday morning at midnight and finishes Monday morning in time for school at 8am?*