Saturday Add-on--More on my [fictional] ancestors

Re: Saturday Add-on--Pacing the floor ...

Larry Barrett

is what I first thought, thinking that when Ben was 5, Jane was 25 and 6 years before that is the day Ben was born. But I don't think the years match up.

Close!

Alex Y

But check the age difference.

Re: Close!

Ed in Leaside

Yes, 5x21-6=99. But what does this have to do with her husband?

Re: Close!

Larry Barrett

Jane was born on first Sunday of the year in 1897. Checking a calendar, that was on Jan 3, 1897. So she would be 25 on Jan 3, 1922.

Ben was born on the 'same day of the year' in 1918. The 'same day of the year' could mean Jan 3, 1918 or could mean the first Sunday of year, 1918, which would have been Jan 6, 1918.

So Ben would be 5 on either Jan 3 or Jan 6, 1923.

The years still don't seem to work out for Jane to be 5 times as old as Ben. Unless Ben was born early in the day on Jan 3 and Jane was born late in the day on Jan 3, so technically Jane would still be 25 at the time Ben was 5 on Jan 3, 1923.

Re: Close!

Alex Y

Exact ages, not ages last birthday.

E.g.

Alex Y

If I were 36 1/2 when my daughter was born, our age difference would always be 36.5 years. When I was 54 3/4, I would have been three times her age (18 1/4).

Re: E.g.

Larry Barrett

I thought that is what you meant. I had to take off my socks and shoes to count all the days, but this is what I came up with:

Counting in the extra days for leap years in 1904, 08, 12, 16, and 20, on Jan 3 1923 Jane would be 9495 days old and Ben would be 1826 days old (or 1823 days old if born on Sunday, Jan 6 instead of Jan 3. 9495/5 = 1899, so at this point, Jane is a little more than 5 times as old as Ben. Is there a day a short time in the future when Jane will be exactly 5 times older than Ben?

(9495 + x)/5 = 1826 + x; solving for x, 1899-1826 = 73 = 4x/5, x = 91.25, and if Ben born on Jan 6 instead, 1899 - 1823 = 76 = 4x/5, x = 95.

So on Jan 3 + either 91.25 days or 95 days, Jane will be exactly 5 times older than Ben. That day will be either April 4 or April 8, 1923.

And 6 years earlier would be either April 4 or April 8, 1917.

April 8 1917 was Easter Sunday. It was also about 9 months before Ben was born.

Solution

Alex Y

Larry got it right, but the solution really doesn't require removing socks to count toes! :-)

Jane was born in 1897

Every year after that, she celebrated her birthday on the same day, and in 1918, on her 21st birthday, Ben was born. (If you want to consider the same day of the year to be the first Sunday, you might be up to 6 days off from the actual birthday, but that is a small enough error not to affect the final answer.)

So Jan was 21 years older than Ben (and the actual dates do not matter)

A little algebraic notation: For any year date x, Jane's age j(x) = Ben's age b(x) + 21.

For the date when Jane was 5 times as old as Ben, we can write

5*b(x) = b(x) +21, and solve for Ben's age as 5 1/4.

Six years before that was 9 months before Ben was born, at which point he as being conceived, hopefully involving my grandfather!