Question

Time seems to pass faster when you are old than it did when you were young. Assume that the length a particular period of time seems to be inversely proportional to your age.At your present age, a day seems like a day, a week seems like a week, and so forth
a)How long will a wek seem to be when you are twice as old as you are now?
b)How long did a week seem to be when you were a tenth as old as you are now?
c)A mother 36 years old says to her 3 year old child dont get your toys out you have only 5 minutes to play. Based on your model and in terms of the mother's time scale, how long does that 5 minutes seem to be to the child? Does this result suggest a reason for some types of parent-child conflicts?

Answer 1

Let the Apparent period of time = T at age Age
T can be a week or a day or one hour or 1 year.
Given t is inversely proportional to age.

$T \alpha \frac{1}{Age} \\ \\ present\ age = Age_{0},\ present\_time\_period = T_{0} \\ \\ T = \frac{T_{0} * Age_{0}}{Age} \\ \\ OR,\ equivalently,\ T * Age = T_0 * Age_0 \\ \\ a)\ \ Age = 2*Age_0 \\ \\ T = \frac{1\ week\ *\ Age_0}{2\ *\ Age_0} \\ \\ T = \frac{1}{2} Week \\ \\ A\ week\ will\ seem\ to\ be\ just\ half\ of\ a\ week.\\ \\ b) \ T = \frac{1 week * Age_0}{\frac{Age_0}{10}} = 10 * week \\ \\ So\ a week\ appeared\ to\ be\ as\ long\ as\ 10\ weeks.$

$T = \frac{5 \ minutes * 36\ years}{3 years} = 60 minutes = 1 hour$

When a 3 year old child accompanies her/his mother (36 yrs) to a market or friends house, the mother spends 5 minutes conversing with her friend.  That duration seems to be as long as 1 hour to the child.  So the child gets annoyed and bored.