How Old Did This Man Live to Be?

Date: 02/23/98 at 20:57:54
From: Christine Maruna
Subject: Math

I am trying to find the age of this person: he spent 3/13 of his life 
at school, 4/39 of his life in medical school, 1/2 his life as a 
surgeon, and he died 13 years into retirement. How old did he live to 
be?

I don't know where to begin this problem. Thank you.

Date: 02/27/98 at 10:03:53
From: Doctor Jen
Subject: Re: Math

Hi there, 

I'd start by saying that ALL the parts of his life add up to 1. 

So you know that 3/13 + 4/39 + 1/2 + R = 1, where R is the fraction of 
his life he spent in retirement.

We want to find the fraction that his retirement represents, because 
we know how many years his retirement lasted. So if we know that 
fraction, we can work out how long his total life was.

Let's rearrange the equation to work out R. Take the fraction terms on 
the left side over to the right side:

This gives us R = 1 - 1/2 - 4/39 - 3/13.

Now we need to add the terms on the right side to find R. Are you okay 
with adding fractions? I'd imagine you are, if you're being asked 
questions like this.

We know the length of his retirement was 13 years, and we know that 13 
years represents R of his life: R*L, if L is the length of his life. 
You can use that information to work out just how long his life was. 
R*L = 13, and you know R, so L = ? 

Good luck...

-Doctor Jen, The Math Forum
 Check out our web site http://mathforum.org/dr.math/