To solve the problem using the guess and check method, we'll need to verify how many miles each bird flew based on different time combinations. The total distance flown by each bird can be calculated using the formula:
\[ \text{Distance} = \text{Rate} \times \text{Time} \]
Here are the known constants:
- Speed of goose = 20 mph
- Speed of heron = 10 mph
- Total time = 14 hours
- Total distance apart = 180 miles
Now, let's check the proposed solutions:
-
3 hours (goose) and 11 hours (heron):
- Distance flown by goose: \( 20 \text{ mph} \times 3 \text{ h} = 60 \text{ miles} \)
- Distance flown by heron: \( 10 \text{ mph} \times 11 \text{ h} = 110 \text{ miles} \)
- Total distance = \( 60 + 110 = 170 \text{ miles} \) (not correct)
-
6 hours (goose) and 8 hours (heron):
- Distance flown by goose: \( 20 \text{ mph} \times 6 \text{ h} = 120 \text{ miles} \)
- Distance flown by heron: \( 10 \text{ mph} \times 8 \text{ h} = 80 \text{ miles} \)
- Total distance = \( 120 + 80 = 200 \text{ miles} \) (not correct)
-
4 hours (goose) and 10 hours (heron):
- Distance flown by goose: \( 20 \text{ mph} \times 4 \text{ h} = 80 \text{ miles} \)
- Distance flown by heron: \( 10 \text{ mph} \times 10 \text{ h} = 100 \text{ miles} \)
- Total distance = \( 80 + 100 = 180 \text{ miles} \) (correct)
-
5 hours (goose) and 9 hours (heron):
- Distance flown by goose: \( 20 \text{ mph} \times 5 \text{ h} = 100 \text{ miles} \)
- Distance flown by heron: \( 10 \text{ mph} \times 9 \text{ h} = 90 \text{ miles} \)
- Total distance = \( 100 + 90 = 190 \text{ miles} \) (not correct)
Based on the calculations, the correct answer is 4 hours for the goose and 10 hours for the heron.
2 answers