Question

A Canadian Goose and Great Blue Heron took off in opposite directions. The goose flew at 20 mph, and the heron flew at 10 mph. When they landed, they were 180 miles apart. Altogether, they flew for 14 hours. How long did each bird fly?


Use the guess and check method to solve this problem.

A Canadian Goose and Great Blue Heron took off in opposite directions. The goose flew at 20 mph, and the heron flew at 10 mph. When they landed, they were 180 miles apart. Altogether, they flew for 14 hours. How long did each bird fly?


3 hours (goose) and 11 hours (heron)


6 hours (goose) and 8 hours (heron)


4 hours (goose) and 10 hours (heron)


5 hours (goose) and 9 hours (heron)

Answer 1

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:

1. **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)

2. **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)

3. **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)

4. **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**.