https://file.aiquickdraw.com/mathbot/file/1728393521051gi22gued.jpg

Let's analyze the question and the distance-time graph from the image you provided.

### Key Observations from the Graph:
1. **Time** is on the horizontal axis (in minutes).
2. **Distance** is on the vertical axis (in kilometers).
3. The graph is divided into three main segments:
   - First segment: Asha drives from her home to the airport.
   - Second segment: Asha waits at the airport (flat line, no movement).
   - Third segment: Asha drives back home.

### Steps to Calculate the Distance:
We know the **average speed** of the entire journey is 48 km/h. The total time of the journey can be derived from the graph:
- Asha drives to the airport in 60 minutes (from 0 to 60).
- She waits at the airport for 60 minutes (from 60 to 120).
- She drives back home in 60 minutes (from 120 to 180).

The total journey time is \( 180 \) minutes, or \( 3 \) hours.

### Formula for Average Speed:
The formula to calculate the average speed is:

\[
\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}
\]

We are given that the average speed is **48 km/h**, and the total time is \( 3 \) hours, so we can calculate the **total distance** of the journey:

\[
48 = \frac{\text{Total Distance}}{3}
\]

\[
\text{Total Distance} = 48 \times 3 = 144 \text{ km}
\]

Since the total distance is **144 km** and Asha drives to the airport and back (round trip), the distance **from Asha's home to the airport** is half of the total distance:

\[
\text{Distance to the airport} = \frac{144}{2} = 72 \text{ km}
\]

### Final Answer:
The distance from Asha’s home to the airport is **72 km**.

Would you like further clarification on any part of the solution?

---

Here are 5 related questions to deepen your understanding:
1. How would the total distance change if Asha had driven back slower than she went to the airport?
2. Can you calculate Asha’s speed during the first leg of her journey based on the graph?
3. If Asha waited at the airport for 90 minutes instead of 60, how would that affect the average speed?
4. What is the significance of the flat section of the graph in terms of her journey?
5. How could you determine the speed during each segment of the journey using the graph?

### Tip:
When analyzing distance-time graphs, the slope of the line represents the speed of the object. The steeper the line, the faster the object is moving.

Asha drove to the airport from her home. She waited at the airport and then drove home. The average speed of the journey was 48 km/h. What is the distance from Asha's home to the airport?

This problem focuses on calculating the distance from Asha’s home to the airport using the average speed of 48 km/h and a distance-time graph. Suitable for students in Grades 6-8, it covers the concepts of distance-time graphs and average speed.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation