We gave our old iPhones to our kids this year, and got ourselves new ones through a deal with the provider. Now, in the quarto iPhone household we have constant fights over who gets to charge first. We do have enough chargers but some of them are located in more convenient places than others: kitchen and car chargers are the most popular.

The other day our son gets into a car and screams in panic that he has only 40% battery left and needs the charger while my phone that is 20% full has just been plugged in. The truth is on my side, right? But the problem is not as simple. His older iPhone is losing power much faster than my iPhone 4G, even when they run idle. On average it takes his phone 2.5 days to run out of battery while for my phone it is 6 days. So, who deserves the charger?

Image by Sixth Lie, distributed under CCL.

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

The other day our son gets into a car and screams in panic that he has only 40% battery left and needs the charger while my phone that is 20% full has just been plugged in. The truth is on my side, right? But the problem is not as simple. His older iPhone is losing power much faster than my iPhone 4G, even when they run idle. On average it takes his phone 2.5 days to run out of battery while for my phone it is 6 days. So, who deserves the charger?

Image by Sixth Lie, distributed under CCL.

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

## 14 comments:

Well your son deserves the charger as his mobile's life is only one day whereas your mobile's life is 1.2 days

Like this as a context. I made a GeoGebra sketch to let students investigate. (Although it shows the answer to start.) http://www.geogebratube.org/student/m11757

Needless to say, you should give your son the charger. Once he asks politely.

Let's make some assumptions:

1) "Run out" means 0% battery

2) "days" for both phones are exactly 24 hours

3) When you averaged the time it took to run out, the phones started @ 100%

4) The loss rate is constant within each phone.

So, for the son's phone, it takes 2.5 days or 60 hours to go from 100 % to 0%. Divide 100% by 60 to get a loss rate of 1.66% per hour. With 40% remaining on his phone, he has 40% / 1.66% per hour, or 24.1 hours of battery life left.

For Mom's phone, it takes 6 days or 144 hours to got from 1005 to 0%, a loss rate of (100/144) or 0.694% per hour. With 20% remaining, Mom has 20%/0.694% per hour, or 28.8 hours of battery life remaining.

So, the son should get priority for the charger!

He deserves the charger. His phone has only 1 day of charge left (2.5 * 0.4), while yours has 1.2 days left (6 * 0.2).

I wonder if I understand this correctly.

Your phone has only 20% of it's charge left. Since you are good for 6 days that means you have 6*20/100 = 1.2 days left.

Your son has 40% left but his phone has a charge life of 2.5 days which means he has only 1 day left before his phone dies.

But I wonder if the 20 / 40 ratio also represent the amount of time it will take to charge the phones? Do you need the charger 80/60 which means that your time will be 4/3 of his? That brings us to the all important question: do you require more than the day that he has left?

Conclusion

If all you are concerned about is who runs out first, he will.

If you are concerned about how much time is left before neither of you has a phone, he will again.

If the charge times are equal, then you need the charger for longer than he does [ratio of 4/3].

My advice is to avoid the problem entirely and get one of those Car Cigarette Lighter Triple Socket Adapter with USB Output (Black) found at

http://www.amazon.com/Cigarette-Lighter-Triple-Socket-Adapter/dp/B003174TWE/ref=sr_1_1?ie=UTF8&qid=1339172108&sr=8-1

40% of his battery is one day (1/2.5) of his battery life. 20% of your battery is more than one day of your battery life. Looks like your son is the one who deserves the charger.

I think your son should get the charger.

He has 40% left on a phone that has a 2.5 day battery life so he has about 1 day left on the phone. (2.5 x .4 = 1.0) You have 20% left on a phone that has 6 days of battery life or 1.2 days remaining. (6 x .2 = 1.2)

You would both probably make it through the day but with all you son's texting, phoning, googling, etc. he might use it up quicker than the avg. user and I'm assuming you may not use your phone as much as he. Not to mention it may avoid a nice argument! (And I'm assuming this is not a school day which would bring up other, less mathematical, considerations!)

this is my son's answer(Ben, 11):

the person who should recieve the charger is the son. when i first read it i saw that the son was at 40% and the mom was at 20%, so i automaticly knew that the awnser should be under half of the maximum time.then i saw that the mom's phone could last for 6 days at full charge and that 20% is 1/5 of 100% so i took 6 and divided it into 5 and got 1.2. Next i saw the sons maximum time at 100% was 2.5 days. so i cut 2.5 in half and got 1.25 now i needed 10% of 2.5 and i knew it was 0.25 because 0.25 x 10 = 2.5. so i removed 0.25 from 1.25 and got 1.00. so for mom it could last fro 1.2 days or 1 1/5 days, and for the son it would last for 1 day. Therefore the charger should go to the son considering that his phone would run out first.

Son's iPhone battery lasts 2.5 days

Mom's iPhone battery lasts 6 days

Assuming that the battery discharge is linear:

- Son's battery discharges 20% of the battery each 0.5 days.

- Mom's battery discharges 20% of the battery each 1.2 days.

Son has 40% of battery left, so his battery is good for 1.0 more days.

Mom has 20% of battery left, so her battery is good for 1.2 more days.

Based on remaining battery life alone, son should have priority for the charger.

However, there are many other considerations:

* Are both people using their phone to the same degree for important (calling-related) uses and for games? Important uses should be given priority.

* Who is going to be needing to use their phone more in the next day or so? For example, is one person traveling? (and therefore harder to reach by other means) Or will one person be somewhere (school) where they won't be able to use their phone during the day?

* Who is going to have more access to other phones/landlines for calls in the next day?

Given these types of considerations, I would probably let you the mom charge your phone first ahead of your son... .and not just because I am a mom too.

TracyZ

I love you guys: a lot of good math, geometrical sketches, parenting advice, and even a pointer to a triple charger. Thank you!

To add to all this here are a few points from my brother-in-law:

1. Loosing energy from your batteries is not linear.

2. Charging pace is also not linear.

3. Not only older batteries discharge faster, but charging pace is slower as well.

So, assuming or approximating a linear loss of charge, my son deserves the charger as his phone will run out of a battery sooner. You all were right. In reality I think it is not a linear but highly dependent on the number of activities one is doing - games, messages, mail, internet browsing.

If we will take into account that his older phone may be charging at a slower pace then one can make a point that he should give me the charged as in a car it is better to have one fully charged phone than two barely charged.

A puzzle point for everyone and especially for Anne-Marie's son Ben.

Dear Maria,

What about the other chargers in the house. I'm confused why you or your son can't just use those. Either you could use the one in the car or kitchen or he could use the one in the car or kitchen.

P.S. I do love your puzzles. Especially since I love math! Thanks.

Dear Maria,

I was wondering, where do you find these puzzles? I just love them. Please tell me. Thank you,

Hibah

Hi Hibah - welcome to this puzzle marathon. I am glad you like puzzles. I am trying to invent most of them using daily life experiences. If you'll pay close attention you'll notice those puzzles hiding in every corner of your life as well.

Regarding chargers - the puzzle deals with the specific situation of two people with two cells in one car with one charger. See the answers above.

best!

Maria TheMathMom

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