Question 641184
To solve, let's turn the sentences into equations.  The first sentence says that one number is 3 times another.  In other words:

x = 3y

The next sentence says that the sum of their reciprocals is 20/3. In other words:

{{{1/x + 1/y = 20/3}}}

To solve, we need to substitute x in the second equation, with 3y, that way we will get rid of x and solve for y:

{{{1/3y + 1/y = 20/3}}}

Next, multiply the equation by 3y.  This will get rid of our fractions and leave us with:

{{{1 + 3 = 20y}}} =

{{{4 = 20y}}}

Divide both sides of the equation by 20, and this will leave us with y, which will be one of our numbers:

{{{y = 4/20}}} = {{{y = 1/5}}}

So, 1/5 is one of our numbers.  

We know that the other number is 3 times y.  So, 3 x 1/5 will give us our other number:

3 x 1/5 = 3/5

FINAL ANSWER:  1/5 and 3/5 are the numbers