After spending the winter in Fulton County, two flocks of birds are now migrating home. The first flock flies due east at 33 kilometers per hour, and the second flies west at 63 kilometers per hour. In how much time will they be 390 kilometers apart?

Question

If necessary, round your answer to the nearest minute.
hours and
minutes

Answer 1

To solve the problem, we first need to determine the speed at which the two flocks of birds are moving apart from each other.

• The first flock is flying east at 33 kilometers per hour.
• The second flock is flying west at 63 kilometers per hour.

Since they are flying in opposite directions, we can add their speeds to find the total speed at which they are moving apart:

\[ \text{Total speed} = 33 , \text{km/h} + 63 , \text{km/h} = 96 , \text{km/h} \]

Next, we need to determine how long it will take for the two flocks to be 390 kilometers apart. We can use the formula:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

Substituting the values we have:

\[ \text{Time} = \frac{390 , \text{km}}{96 , \text{km/h}} \approx 4.0625 , \text{hours} \]

Now, we convert 4.0625 hours into hours and minutes. The integer part of 4.0625 is 4, so we have 4 hours.

To convert the decimal part (0.0625 hours) into minutes, we multiply by 60:

\[ 0.0625 , \text{hours} \times 60 , \text{minutes/hour} = 3.75 , \text{minutes} \]

Rounding 3.75 minutes gives us approximately 4 minutes.

Thus, the total time until the two flocks are 390 kilometers apart is:

\[ \text{4 hours and 4 minutes} \]

Therefore, the answer is:

4 hours and 4 minutes.