Long ago, I was a math teacher. These days, I tutor part-time and (try to) focus on my writing career.
One of the great things about tutoring is that, unlike classroom teaching, there is very little prep-time. I just show up and help kids with their homework, or force them to organize their binders. Normally, we work on whatever they happen to be doing in class. And if all else fails, we review fractions and do mental math because every middle school student needs practice with fractions and mental math. Take it from one who knows.
Still, occasionally I spend a little of my own time browsing the Internet to find activities I can do with my students, which is how I found this page of “classic problems” from Ask Dr. Math. I was intrigued by one I’d never heard of called “Camel and Bananas.” I skimmed the first two sentences and thought it sounded interesting. Granted, I was largely swayed by my love of both camels and bananas, plus how ridiculously charming the two sound together, but in any case, I decided to work on the problem with one of my students.
That afternoon I had my student read the problem out loud:
A camel must travel 1000 miles across a desert to the nearest city. She has 3000 bananas but can only carry 1000 at a time. For every mile she walks, she needs to eat a banana. What is the maximum number of bananas she can transport to the city?
As my student was reading, it suddenly occurred to me: I had no idea how to solve this problem. In fact, it seemed impossible. If the freakin camel has to eat a banana for every mile she travels, and she can only carry 1000 bananas at a time… then by the time she reaches the city, she will have eaten all of her bananas!
My student seemed to have surmised this as well. She looked at me with a baffled expression.
I looked back at the website. Oh, thank god, there was more information! I read it out loud:
Let’s begin by imagining how the camel might get the bananas across the desert. If she starts off with 1000 bananas and carries them 1000 miles, she won’t be able to return for the rest of them because she won’t have any bananas to fuel her trip back. She won’t have any bananas to give to her friends either, because she will have eaten them all during the journey. This suggests that the camel needs to cache piles of bananas at certain points in the desert so she can actually move some of them instead of using them all for fuel.
“Oh, I see!” I said, half to my student and half to myself. “She has to leave little piles of bananas in the desert and make more than one trip!”
My student was still looking baffled.
“Come on,” I said, getting excited. “Let’s try a few things and see what we find out. Let’s just pick a place for her to leave some bananas. What do you think? 50 miles? 200 miles?”
She shrugged. “200 miles?”
“Great!” I grabbed a piece of scratch paper. “So the camel takes 1000 bananas 200 miles into the desert. She eats 200 of them on the way, and then she needs 200 to get back. So how many bananas will she leave in a pile in the desert?”
“Exactly! So then she does it again. She takes another 1000 bananas 200 miles and then goes back…”
“So now she has a stash of 1200 bananas in the desert,” my student says. I wouldn’t say she was excited, but she was certainly amused by my excitement.
We drew this picture:
“Oh no!” I said. “Now she’s got 2000 bananas in a pile 800 miles away from the city, but she can only carry 1000 bananas at a time!”
In this scenario, the camel ends up getting to the city with only 200 bananas. Still, that’s a lot better than none.
“OK, so let’s try it again,” I said. “Except let’s see what happens if she leaves her bananas in a different spot in the desert.”
“OK.” My student said. She was getting into it now (at least I like to think so.)
So we tried leaving the bananas at the 300-mile marker. Turns out, the camel can get 300 bananas to the city that way! Then we tried 350, but that still only yielded 300 bananas to the city.
“So what’s the answer?” my student asked me when we only had five minutes left of class.
“I don’t actually know.”
When I got home, I sat down to work more on the Camel and Bananas problem. I found a way to get 500 bananas to the city – it involves leaving stashes of bananas in various locations in the desert.
When my husband came home, I told him about the problem (he’s got a Master’s degree in Applied Mathematics), and he got to work, creating an infinite series that he thought would solve the problem.
Finally, I googled the answer and wanted to smack myself for not realizing what I should have done. In all of my attempts, the camel made a total of three trips. After all, there were 3000 bananas, and she could carry 1000 at a time. But in order to get the maximum number of bananas to the city, the hardworking camel has to make more than three trips!
I know it seems like this post is about math, and it is. But it’s about so much more. It’s about my writing career. It’s about life. It’s about hardworking camels.
I am always in such a hurry to get as many bananas as possible to the city. And by that I mean, I’m always anxious to finish writing novels and get them published. And these days I’ve been down because I feel like I took a big step backwards when I lost my agent. It’s been years since I started focusing on writing, and I have yet to get a book published. I’ve been trekking through the desert for miles, yet I wind up in the city empty-handed.
But this math problem has illuminated everything! Sometimes you go for miles, and then you have to turn around and go back to where you started, leaving your bananas in a pile in the desert. Taking steps backwards might be frustrating, but necessary.
Most importantly, you might have to take multiple trips to find success. Sometimes it takes a lot more trips than you were expecting. And even then, not all your bananas will make it to the city. Not all the books I’ve written will get published. That’s just the way it goes. It’s hard work, but it’s worth it. Getting some of your bananas to the city is better than getting none, and if it takes a bunch of trips — so be it. Enjoy the desert sunsets along the way.
As for the answer to the problem, I’ll let you work on that yourself. I’ll just say this: the maximum number of bananas the camel can get to the city is more than 500, and it takes her more than three trips. Happy problem-solving!