Question

on a recent business trip, a salesman traveled 52 miles the first hour, 64 miles the second hour, and 49 miles the third hour. how many miles did he average per hour?

64 mph
55 mph
49 mph

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Rate Word Problems"
],
"new_concepts": [
"Average Speed"
],
"current_concepts": [
"Rate Word Problems",
"Average Speed"
]
}
</pre_analysis>

<reasoning>

Calculate total distance and total time

\[

$$\begin{aligned} d_{\text{total}} &= 52 + 64 + 49 = 165 \text{ miles} \\ t_{\text{total}} &= 1 + 1 + 1 = 3 \text{ hours} \end{aligned}$$

\]

Calculate average speed

\[
\text{Average Speed} = \frac{d_{\text{total}}}{t_{\text{total}}} = \frac{165}{3} = 55 \text{ mph}
\]
</reasoning>

<answer>
<mcq-option>64 mph</mcq-option>
<mcq-correct>55 mph</mcq-correct>
<mcq-option>49 mph</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Average Speed"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Rate Word Problems"
],
"new_concepts": [
"Average Speed"
],
"current_concepts": [
"Rate Word Problems",
"Average Speed"
]
}
</pre_analysis>

<reasoning>

Calculate total distance and total time

\[

$$\begin{aligned} d_{\text{total}} &= 52 + 64 + 49 = 165 \text{ miles} \\ t_{\text{total}} &= 1 + 1 + 1 = 3 \text{ hours} \end{aligned}$$

\]

Calculate average speed

\[
\text{Average Speed} = \frac{d_{\text{total}}}{t_{\text{total}}} = \frac{165}{3} = 55 \text{ mph}
\]
</reasoning>

<answer>
<mcq-option>64 mph</mcq-option>
<mcq-correct>55 mph</mcq-correct>
<mcq-option>49 mph</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Average Speed"
]
}
</post_analysis>