Let's define the two numbers as follows:

• Let the smaller number be $x$.
• The larger number is four times the smaller number, so it will be $4x$.

The problem states that the difference between the two numbers is 60. This means:

$4x - x = 60$

Now, solve for $x$:

$3x = 60$

$x = \frac{60}{3} = 20$

So, the smaller number is $20$, and the larger number is:

$4x = 4 \times 20 = 80$

Thus, the two numbers are $20$ and $80$.

Would you like a more detailed explanation or further help with similar problems?

Related Questions:

1. What would happen if the larger number were three times the smaller number instead of four?
2. How would you solve this if the difference was 100 instead of 60?
3. What is the general approach to solving word problems involving relationships between two numbers?
4. If the difference between two numbers is 60 and the larger is twice the smaller, what would the numbers be?
5. How can we represent such problems using algebraic equations?

Tip: When solving word problems, always start by defining the unknowns and translating the problem into an equation, then solve step-by-step.