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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Let's break down the problem step by step.

1. **First Part of the Trip (Away from Home):**
   - John drives for 3 hours at a speed of 60 mph.
   - Distance traveled = speed × time = 60 mph × 3 hours = 180 miles.
   - So, John is 180 miles away from home after the first part.

2. **Second Part of the Trip (Returning Home):**
   - John tries to get home in 4 hours.
   - **First 2 hours:** He is in standstill traffic, so he doesn't move.
     - Distance covered in these 2 hours = 0 miles.
   - **Next half-hour (0.5 hours):** He drives at 30 mph.
     - Distance covered = 30 mph × 0.5 hours = 15 miles.
   - **Remaining time:** Total time for the return trip is 4 hours. He has already spent 2.5 hours (2 hours in traffic + 0.5 hours driving), so the remaining time is 4 - 2.5 = 1.5 hours.
     - He drives at 80 mph for these 1.5 hours.
     - Distance covered = 80 mph × 1.5 hours = 120 miles.

3. **Total Distance Covered on the Return Trip:**
   - Distance covered = 0 miles (traffic) + 15 miles (driving at 30 mph) + 120 miles (driving at 80 mph) = 135 miles.

4. **Distance from Home at the End of the 4 Hours:**
   - Initial distance from home = 180 miles.
   - Distance covered on the return trip = 135 miles.
   - Remaining distance from home = 180 miles - 135 miles = 45 miles.

So, John is 45 miles away from home at the end of those 4 hours.

$\boxed{45}$