Today is my daughter’s birthday. Happy birthday, Elisabeth!
Awake in the wee hours recently, I got to thinking about birthdays. Birthday math, actually.
Like a few years ago when my wife Cheryl and I celebrated our 100th birthday together! We were born in the same year, just over six months apart. So I realized that somewhere between our 50th birthdays there would be a day when the sum of our ages equaled exactly 100 years. I calculated the date and we went out for a special dinner that night.
Another time just a couple of years back, my friend Brian and I went for a “ride your age” bike ride. The year prior we’d gone riding together on my birthday and he’d laid down the challenge. When we got together for a “birthday ride” one year later, we agreed that neither of us was ready to ride 64 miles that day. So we rode 32 miles and added it together!
My daughter and my mom both have birthdays in August and this month mom celebrates her 90th birthday. So – back in the wee hours – I got to thinking about “when would Elisabeth be half her grandmother’s age?” I started plugging in numbers in my head and wasn’t getting anywhere. Then I saw that it’s a simple algebraic equation, so I set it up in my mind and worked the numbers to calculate the value of X. I’m not about to give away my grown daughter’s age, so I’ll just leave it at that …
But that thought stream led me to another birthday math challenge, which I can share. My grandson Ransom celebrated his 21st birthday on February 2nd this year while studying in China. I celebrated my 66th on June 14th – and “rode my age” in the Cartersville Century bike ride just two weeks later! So, here’s the puzzle. On what date will Ransom be exactly half my age?
Well, I got it close… In 2037 Ransom will turn 45, you will have your 90th birthday, Dad… and if I make it that long, I will turn 68. So there’s some more birthday math to ponder. 🙂
Hi, Philip! Thanks for weighing in. When pondering this in the wee hours one morning I’d calculated 2037 as well. The question I posed was, “When will Ransom be half my age?” And the algebraic equation I set up in my mind was: Ae + x = 2(Ar + x), where A is current age for me and him respectively and x is a number of years from now. But if you look closely at the birthdays, Ransom will turn 45 BEFORE I turn 90. Therefore, the actual date when he’s exactly half my age must PRECEDE both our birthdays. It’s a matter of days …
That’s a tricky one, Dad! I think it’s April 7th, 2037 — midway between Ransom’s birthday and yours, considering 2037 is not a leap year. Love you!
You’re on the right track, Lissa! And 2037 seems to have potential as the calendar year part of the solution. (In thinking it through, I considered leap years as well and may or may not have factored that appropriately in my own solution.) But the key is to realize that the date Ransom becomes exactly the same age I was on the day he was born is the date he will be exactly half my age. I found this to be a separate calculation from the year, because we cannot easily apply decimal fractions to years. It remains a matter of days …
This was a fun problem! If you round it out to years, it’s 2037. But since you all are attempting to get the exact answer, I thought I’d take a stab at it.
Using wolframalpha (a magical tool. Without coffee and wolfram, I’d have no chance of finishing my degree), I calculated the number of days between june 14th, 1947 and feb 2nd, 2037 (I estimated the actual date would lie closer to my birthday than Papa E’s) and feb 2nd, 1992 and feb 2nd, 2037. The answers, respectively, were 32741 and 16437. Now the answer can be found with the equation below. X is the number of days between 2/2/37 and the actual date when I will have lived half as many days as Papa E
days between my birth and my 45th birthday + X = (days between Papa E’s birthday and my 45th birthday + X) / 2
So I plugged 16437 + x = (32741 + x) /2 into wolfram, and it told me that x = -133. The date we’re looking for is 133 days before my 45th birthday. Use wolfram again (“133 days before feb 2nd, 2037”) and the answer is Monday, September 22nd, 2036.
Now who wants to calculate the time? I was born at 2:22 am 🙂
Splendid solution, Ransom! And correct as near as I can tell.
I’ve tackled this on two separate occasions – both times tumbling the numbers in my head – and twice came up with September 23, 2036.
The difference probably has to do with how each approach “counts” the respective “start from” dates – are they “zero” or “one” in value? I’m game to go with your solution: September 22, 2036. Where shall we have the party?
Just checked the work using:
http://www-users.med.cornell.edu/~spon/picu/calc/agecalc.htm
Great work Ransom!! Only 24 years and 2 days to go. I wonder at what time you will be half his age?