Question 288281
Say that one of the number is A, and the other is B. 

A is three times the other number:
A = 3B

The reciprocal of a number is another number which, if multiplied by that number, would yield 1. The reciprocal of A would be 1/A, and the reciprocal of B would be 1/B.

First, finding the value of B:

{{{(1/A) + (1/B) = 1/6}}}
{{{(1/3B)+(3/3B)=1/6}}}
{{{4/3B=1/6}}}

This would yield:
{{{4*6=3B*1}}}
{{{B=24/3}}}
Therefore, <b>B = 8</b>

{{{A=3B=3*8}}}
Therefore, <b>A = 24</b>