Let \( t \) be the time (in hours) that the Canadian goose flew. Then, the time that the great blue heron flew would be \( 14 - t \) hours (since they flew for a total of 14 hours).
The distance flown by the goose can be calculated as:
\[ \text{Distance of goose} = \text{Speed of goose} \times \text{Time flown by goose} = 20t \]
The distance flown by the heron can be calculated as:
\[ \text{Distance of heron} = \text{Speed of heron} \times \text{Time flown by heron} = 10(14 - t) \]
Since the distances flew by both birds add up to 180 miles, we can set up the equation:
\[ 20t + 10(14 - t) = 180 \]
Now, let's simplify and solve for \( t \):
\[ 20t + 140 - 10t = 180 \]
Combine like terms:
\[ 10t + 140 = 180 \]
Subtract 140 from both sides:
\[ 10t = 40 \]
Now, divide by 10:
\[ t = 4 \]
So, the Canadian goose flew for 4 hours. To find the time the heron flew, we subtract this from 14:
\[ 14 - t = 14 - 4 = 10 \]
The great blue heron flew for 10 hours.
In summary:
- The Canadian goose flew for 4 hours.
- The great blue heron flew for 10 hours.
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