Question

Multiple Representations  The equation yequalsStartFraction 10 Over 20 EndFraction
x describes the number of kilometers y that a van travels in x minutes. What is the constant speed of the van in terms of​ hours? Use pencil and paper. Express the speed in three different ways.
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Part 1
The constant speed of the van is
  
enter your response here kilometers per hour.

Answer 1

To find the constant speed of the van in kilometers per hour, we'll start with the given equation:

\[
y = \frac{10}{20} x
\]

This simplifies to:

\[
y = 0.5x
\]

This means that for each minute \( x \), the van travels \( y \) kilometers, where \( y \) is equal to \( 0.5x \).

### Step 1: Determine Speed in Kilometers per Minute

From the equation, we see that in 1 minute, the van travels:

\[
0.5 \text{ kilometers}
\]

### Step 2: Convert Minutes to Hours

There are 60 minutes in one hour, so to find the speed in kilometers per hour, we multiply the speed in kilometers per minute by the number of minutes in an hour:

\[
\text{Speed (km/h)} = 0.5 \, \text{km/min} \times 60 \, \text{min/h}
\]

Calculating this gives:

\[
\text{Speed (km/h)} = 0.5 \times 60 = 30 \, \text{km/h}
\]

### Summary of the Answers

1. **Speed in Kilometers per Hour**:
\[
30 \, \text{km/h}
\]

2. **Speed in Kilometers per Minute**:
\[
0.5 \, \text{km/min}
\]

3. **Speed in Meters per Second**: To convert kilometers per hour to meters per second, use the conversion \( 1 \text{ km/h} = \frac{1}{3.6} \text{ m/s} \).

\[
30 \, \text{km/h} = \frac{30}{3.6} \approx 8.33 \, \text{m/s}
\]

### Conclusion

The constant speed of the van can be expressed in three different ways:

1. **Kilometers per Hour**: \( 30 \, \text{km/h} \)
2. **Kilometers per Minute**: \( 0.5 \, \text{km/min} \)
3. **Meters per Second**: \( 8.33 \, \text{m/s} \)