Distance Calculation: Jorden's Trip To The Store

Hey everyone! Today, we're diving into a classic math problem that involves speed, time, and distance. It's a scenario many of us can relate to: a trip to the store and back. Let's break down this problem step-by-step and figure out how far Jorden lives from the store. So, buckle up and let's get started!

Understanding the Problem

The problem states that Jorden drives to the store at a speed of 30 miles per hour. On her way back home, she encounters some traffic, which reduces her average speed to 20 miles per hour. The entire round trip takes her half an hour (30 minutes). The million-dollar question is: how far does Jorden live from the store?

To solve this, we need to use the fundamental relationship between distance, speed, and time, which is: Distance = Speed × Time. We'll also use a table to organize the information, making it easier to visualize and work with.

Setting Up the Table

Let's create a table to organize the information we have. This will help us break down the problem into smaller, manageable parts. The table will have columns for direction (to store and from store), rate (speed), time, and distance. Filling out the rate column is our first task.

As you can see, we've already filled in the 'Rate' column with the speeds provided in the problem: 30 mph to the store and 20 mph from the store. Now, let's move on to the next step: figuring out the time for each leg of the journey.

Delving Deeper: Time and Distance

Calculating Time

This is where things get a little more interesting. We know the total time for the round trip is 30 minutes, which is equal to 0.5 hours. However, we don't know how much time Jorden spent driving to the store and how much time she spent driving back. Let's use a variable to represent the unknown time. Let's say:

• t = Time (in hours) Jorden spent driving to the store.

Since the total driving time is 0.5 hours, the time she spent driving back from the store would be:

• 0.5 - t = Time (in hours) Jorden spent driving from the store.

Now we can add this information to our table:

Expressing Distance

Remember the formula: Distance = Speed × Time. We can now express the distance for each leg of the trip:

• Distance to the store: 30 * t
• Distance from the store: 20 * (0.5 - t)

We can now fill in the 'Distance' column in our table:

Solving the Equation: The Key to the Problem

Here's the crucial part: the distance to the store is the same as the distance from the store. This is because Jorden is traveling the same route in both directions. So, we can set up an equation:

30t = 20(0.5 - t)

Now, let's solve for t:

1. Expand the equation: 30t = 10 - 20t

2. Add 20t to both sides: 50t = 10

3. Divide both sides by 50: t = 10 / 50 t = 0.2 hours

So, Jorden spent 0.2 hours driving to the store. Now we can calculate the distance.

Finding the Distance: The Final Step

We can use either the distance to the store or the distance from the store formula to find the answer. Let's use the distance to the store formula:

Distance = 30t

Substitute t = 0.2:

Distance = 30 * 0.2 Distance = 6 miles

Therefore, Jorden lives 6 miles from the store!

Another way to find the Distance

We can use the distance from the store formula to check our solution:

Distance = 20 * (0.5 - t)

Substitute t = 0.2:

Distance = 20 * (0.5 - 0.2) Distance = 20 * 0.3 Distance = 6 miles

As you can see, we arrive at the same answer, which confirms our solution.

Conclusion: Math in Real Life

Isn't it amazing how math can help us solve real-world problems? By breaking down the problem into smaller steps, using a table to organize the information, and applying the fundamental relationship between distance, speed, and time, we were able to determine that Jorden lives 6 miles from the store.

Key Takeaways:

• Understanding the relationship between distance, speed, and time is crucial for solving these types of problems.
• Using variables to represent unknown quantities can help simplify the problem.
• Setting up equations based on the given information is key to finding the solution.
• Always double-check your answer to ensure it makes sense in the context of the problem.

So, the next time you're on a trip, think about how math is at play! Keep practicing, and you'll become a pro at solving these kinds of problems. Keep exploring and have fun with math, guys! Remember, every problem is a puzzle waiting to be solved!