Type the missing number to complete the proportion. 84 kilometers in 8 minutes = 21 kilometers in ___ minutes.
Understand the Problem
The question is asking to find the missing time in minutes that corresponds to 21 kilometers based on the given proportion of distance and time (84 kilometers in 8 minutes). We will use cross-multiplication to solve for the unknown value.
Answer
The missing number is $2$.
Answer for screen readers
The missing number is $2$.
Steps to Solve
- 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.
- Cross-Multiply
To solve for $x$, we will cross-multiply:
$$ 84 \text{ km} \cdot x \text{ min} = 21 \text{ km} \cdot 8 \text{ min} $$
- Calculate the Right Side
Calculate $21 \text{ km} \cdot 8 \text{ min}$:
$$ 21 \text{ km} \cdot 8 \text{ min} = 168 \text{ km} \cdot \text{ min} $$
- Divide Both Sides to Solve for x
Now, isolate $x$ by dividing both sides by 84 km:
$$ x = \frac{168 \text{ km} \cdot \text{ min}}{84 \text{ km}} $$
- Simplify the Expression
Now simplify the expression:
$$ x = 2 \text{ min} \cdot 8 = 2 \text{ min} $$
So, $x = 2 \text{ min}$.
The missing number is $2$.
More Information
The calculation shows that 21 kilometers take 2 minutes to travel at the same speed as 84 kilometers in 8 minutes. Using proportions is a useful method to solve similar problems involving ratios.
Tips
- Forgetting to cross-multiply correctly.
- Miscalculating the multiplication or division, especially with units.
- Confusing the values of the given proportion.