gsm8k-0008

# GSM8K Problem 9

John drives for 3 hours at a speed of 60 mph and then turns around because he realizes he forgot something very important at home.  He tries to get home in 4 hours but spends the first 2 hours in standstill traffic.  He spends the next half-hour driving at a speed of 30mph, before being able to drive the remaining time of the 4 hours going at 80 mph.  How far is he from home at the end of those 4 hours?

Reason step by step, then give ONLY the final answer on the last line as \boxed{ANSWER}.

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To determine how far John is from home at the end of the 4 hours, let's break down his journey step by step.

1. **Initial Drive Away from Home:**
   - **Time:** 3 hours
   - **Speed:** 60 mph
   - **Distance Traveled:** \(3 \text{ hours} \times 60 \text{ mph} = 180 \text{ miles}\)

2. **Return Journey:**
   - **Total Time Available:** 4 hours
   - **First 2 Hours:** Standstill traffic (0 mph)
     - **Distance Traveled:** \(2 \text{ hours} \times 0 \text{ mph} = 0 \text{ miles}\)
   - **Next 0.5 Hours:** Driving at 30 mph
     - **Distance Traveled:** \(0.5 \text{ hours} \times 30 \text{ mph} = 15 \text{ miles}\)
   - **Remaining Time:** \(4 \text{ hours} - 2 \text{ hours} - 0.5 \text{ hours} = 1.5 \text{ hours}\)
     - **Speed:** 80 mph
     - **Distance Traveled:** \(1.5 \text{ hours} \times 80 \text{ mph} = 120 \text{ miles}\)

3. **Total Distance Traveled on Return:**
   - \(0 \text{ miles} + 15 \text{ miles} + 120 \text{ miles} = 135 \text{ miles}\)

4. **Distance from Home:**
   - John initially drove 180 miles away from home.
   - On the return journey, he covered 135 miles towards home.
   - **Remaining Distance:** \(180 \text{ miles} - 135 \text{ miles} = 45 \text{ miles}\)

\[
\boxed{45}
\]