One number is 6 times another. The sum of their reciprocals is $\frac{14}{3}$. Find the numbers.

The numbers are and

Step 1 ：Let's denote the two numbers as x and y. According to the problem, we have two equations:

Step 2 ：1. \(x = 6y\) (one number is 6 times another)

Step 3 ：2. \(\frac{1}{x} + \frac{1}{y} = \frac{14}{3}\) (the sum of their reciprocals is 14/3)

Step 4 ：We can substitute the first equation into the second one to solve for y, and then substitute y back into the first equation to solve for x.

Step 5 ：Substituting \(x = 6y\) into the second equation, we get \(\frac{7}{6y} = \frac{14}{3}\)

Step 6 ：Solving for y, we get \(y = 0.25\)

Step 7 ：Substituting \(y = 0.25\) back into the first equation, we get \(x = 1.5\)

Step 8 ：Final Answer: The numbers are \(\boxed{1.5}\) and \(\boxed{0.25}\)