https://file.aiquickdraw.com/mathbot/file/1727043591523dxl7ihnx.jpg

The problem provided involves determining the relationship between the time it takes to travel between two cities (A and B) based on two different speeds:

- \( x \) is the time to travel the distance at a speed of 50 km/h.
- \( y \) is the time to travel the same distance at a speed of 100 m/s.

Let's go through the steps:

### Step 1: Convert the units of the speeds
- 50 km/h = \( \frac{50 \times 1000 \, \text{m}}{3600 \, \text{s}} = \frac{50000}{3600} \, \text{m/s} = 13.89 \, \text{m/s} \).
- 100 m/s remains as is.

### Step 2: Use the formula for time
The formula for time, \( t \), when distance and speed are known is:

\[
t = \frac{\text{Distance}}{\text{Speed}}
\]

Let \( d \) represent the distance between city A and city B.

For \( x \):
\[
x = \frac{d}{13.89 \, \text{m/s}}
\]

For \( y \):
\[
y = \frac{d}{100 \, \text{m/s}}
\]

### Step 3: Find the relationship between \( x \) and \( y \)
Now, to determine the relationship between \( x \) and \( y \), divide \( x \) by \( y \):

\[
\frac{x}{y} = \frac{\frac{d}{13.89}}{\frac{d}{100}} = \frac{100}{13.89} \approx 7.2
\]

Thus, \( x \approx 7.2y \).

This means that \( x \) is significantly larger than \( y \), and the most appropriate relationship is:

\[
\boxed{A. \, x > y}
\]

Would you like any more details, or do you have further questions?

Here are 5 questions to expand on this:

1. How is the time to travel affected by increasing speed?
2. Can you calculate the time for specific distances based on the given speeds?
3. What is the conversion process from km/h to m/s?
4. How would the relationship between \( x \) and \( y \) change if the speed for \( y \) were different?
5. Can you explain how the distance factor cancels out in the calculation?

**Tip:** Always ensure that units are consistent before performing any calculations, especially when dealing with speeds and distances!

Diketahui jarak kota A dan kota B adalah km. Jika x adalah waktu tempuh dengan kecepatan 50 km/jam dan y adalah waktu tempuh dengan kecepatan 100 m/detik maka hubungan yang paling tepat antara x dan y adalah ....

Determine the correct relationship between the times it takes to travel between cities A and B at speeds of 50 km/h and 100 m/s. This problem involves unit conversions from km/h to m/s and applying the formula for time. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation