Type the missing number to complete the proportion. 84 kilometers in 8 minutes = 21 kilometers in ___ minutes.

Steps to Solve

1. Set Up the Proportion

We know that 84 kilometers corresponds to 8 minutes. We can set the proportion like this:

$$ \frac{84 \text{ km}}{8 \text{ min}} = \frac{21 \text{ km}}{x \text{ min}} $$

where $x$ is the missing time we want to find.

2. Cross-Multiply

To solve for $x$, we will cross-multiply:

$$ 84 \text{ km} \cdot x \text{ min} = 21 \text{ km} \cdot 8 \text{ min} $$

3. Calculate the Right Side

Calculate $21 \text{ km} \cdot 8 \text{ min}$:

$$ 21 \text{ km} \cdot 8 \text{ min} = 168 \text{ km} \cdot \text{ min} $$

4. Divide Both Sides to Solve for x

Now, isolate $x$ by dividing both sides by 84 km:

$$ x = \frac{168 \text{ km} \cdot \text{ min}}{84 \text{ km}} $$

5. Simplify the Expression

Now simplify the expression:

$$ x = 2 \text{ min} \cdot 8 = 2 \text{ min} $$

So, $x = 2 \text{ min}$.