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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I need to track John's journey step by step to find how far he is from home at the end of 4 hours.

First, let me understand the timeline:
- He drives for 3 hours at 60 mph away from home
- Then he turns around and tries to get home in 4 hours total

Let me calculate his position after the first part of his journey:

Distance traveled away from home in first 3 hours:
Distance = Speed × Time = 60 mph × 3 hours = 180 miles

So he is 180 miles away from home when he turns around.

Now for his return journey (which takes 4 hours total):
- First 2 hours: standstill traffic (0 mph)
- Next 0.5 hours: driving at 30 mph
- Remaining time: driving at 80 mph

Let me calculate the distances for each segment of his return journey:

First 2 hours (standstill): 
Distance = 0 mph × 2 hours = 0 miles

Next 0.5 hours (driving at 30 mph):
Distance = 30 mph × 0.5 hours = 15 miles

Remaining time: 4 hours total - 2 hours - 0.5 hours = 1.5 hours
Distance = 80 mph × 1.5 hours = 120 miles

Total distance traveled toward home:
0 + 15 + 120 = 135 miles

Since he started 180 miles away from home, his final distance from home is:
180 miles - 135 miles = 45 miles

Therefore, he is 45 miles from home at the end of those 4 hours.

$\boxed{45}$