Question 1209951
<pre>
Sorry, your '13' is a typo. I think you accidentally interchanged the digits and
meant to type '31' instead of '13'.

So I will do this problem instead, with '13' changed to '31'.

<font color="green"><b>When Tara was 3 years old Joe was 1/3 of Tara's current age. When Joe was 31 years old 
Tara was 1/3 of his current age. How old are each of them now?</font></b>

T = Tara's present age
J = Joe's present age

<font color="green"><b>When Tara was 3 years old, Joe was...</font></b> 

Let that be x years ago, so T-x=3, and Joe was J-x

<font color="green"><b>...Joe was 1/3 of Tara's current age.</font></b> 

{{{J-x = expr(1/3)*T}}}

<font color="green"><b>When Joe was 31 years old Tara was...</font></b>

Let that be y years ago. Joe was J-y=31 and Tara was T-y

<font color="green"><b>...Tara was 1/3 of his current age.</font></b> 

{{{T-y = expr(1/3)*J}}}

<font color="green"><b>How old are each of them now?</font></b>

{{{system(T-x=3, J-x = expr(1/3)*T, J-y=31, T-y = expr(1/3)*J)}}}, 

Solve that by hand, or put it in any system solver.  There are a number
of them online.

Get J=57, T=45, x=42, y=26

{{{system(T=45,J=57,x=42, y=26)}}} 

Let's check:

<font color="green"><b>When Tara was 3 years old,...</font></b>

Tara is 45, so x=42 years ago she was 45-42 = 3.

That checks. 

<font color="green"><b>Joe was 1/3 of Tara's current age.</font></b> 

Joe is 57, so y=26 years ago, he was 57-26 = 31

So that checks.

<font color="green"><b>When Joe was 31 years old Tara was 1/3 of his (Joe's) current age.</font></b> 

y=26 years ago was when Joe was 31, and Tara was 45-26=19. And sure enough,
19 is 1/3 of 57, which is Joe's present age.   
 
Answer: Tara is 45 and Joe is 57.

Edwin</pre>