A fishing boat leaves port at 11 miles per hour at a bearing of 210 degrees for 2 hours, then turns to a bearing of 250 degrees at 8 miles per hour for 4 hours, and finally changes to a bearing of 280 degrees at 7 miles per hour for 2 hours. At this point, the boat heads directly back to port at a speed of 8 miles per hour. Find the time it takes the boat to return to port as well as the boat's bearing as it does. (I know that the return time is 7.67 hours)

bearing to port = 63°20'

time to port = 7.67 hours

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To find the time it takes for the boat to return to port and its bearing during the return, we can break down the boat's journey into different segments. Let's analyze each segment step by step:

Segment 1: The boat travels at a speed of 11 miles per hour at a bearing of 210 degrees for 2 hours.
Since we know the speed and time, we can calculate the distance traveled using the formula:
Distance = Speed × Time
Distance1 = 11 miles/hour × 2 hours
Distance1 = 22 miles

Segment 2: The boat turns to a bearing of 250 degrees and travels at a speed of 8 miles per hour for 4 hours.
Using the same formula, we can calculate the distance traveled in this segment:
Distance2 = 8 miles/hour × 4 hours
Distance2 = 32 miles

Segment 3: The boat changes to a bearing of 280 degrees and travels at a speed of 7 miles per hour for 2 hours.
Calculating the distance traveled in this segment:
Distance3 = 7 miles/hour × 2 hours
Distance3 = 14 miles

Segment 4: The boat heads directly back to port at a speed of 8 miles per hour.
To determine the time it takes to return to port, we divide the total distance traveled so far (22 + 32 + 14 = 68 miles) by the speed:
Time = Distance / Speed
Time = 68 miles / 8 miles/hour
Time = 8.5 hours

Finally, to find the bearing as the boat returns to port, we subtract the previous bearing (280 degrees) from 180 degrees (to reverse direction):
Bearing4 = 180 degrees - 280 degrees
Bearing4 = -100 degrees

Therefore, the time it takes for the boat to return to port is 8.5 hours, and the bearing as it does is -100 degrees.