Question 489601: My son asked me this on his birthday, yesterday:
His birthday is 31st August, and he was 20yrs old yesterday. Mine is 5th February and I was 41yrs old last birthday. Will there ever be a day when he is exactly half my age? My instinct is that yes, there will, but I don't know how to work it out.
Thanks for any help!
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! your son is 20 years old on august 31.
you are 41 on february 5th.
let's try to simplify this and assume you were both born on the same day.
today you are 41
today he is 20
our assumption is that in x years your son will be half your age.
the formula for this would be:
(x + 20) = 1/2 (x + 41)
we need to solve for x.
multiply both sides of this equation by 2 to get rid of the fractionh.
you get:
2 * (x + 20) = (x + 41)
simplify this equation to get:
2x + 40 = x + 41
subtract x from both sides of this equation to get:
x + 40 = 41
subtract 40 from both sides of this equation to get:
x = 1
your son will be 1/2 your age in 1 year.
he will be 21
you will be 42
now we get to birthdays.
his birthday is august 31.
your birthday is february 5.
he will be 21 on august 31 of 2012
you will be 42 on february 5 of 2012.
for a period of time, you will be 42 and he will still be 20.
on august 31 of 2012 he will be 21 and be half your age.
this will continue until february 5 of 2013 when you become 43 and he will still be 21.
so, from august 31 of 2012 until february 5 of 2013, your son will be half your age.
this assumes the smallest increment you want to get down to is years.
if you want to find the exact month or the exact day when your son will be half your age then the formula needs to be revised to account for that.
i won't get into that unless you ask, but the exact day and hour and minute and second can be determined by use of the same formula modified for the increments involved.
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