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After spending the winter in Fulton County, two flocks of birds are now migrating home. The first flock flies due east at 3333 kilometers per hour, and the second flies west at 6363 kilometers per hour. In how much time will they be 390390 kilometers apart? If necessary, round your answer to the nearest minute.\newline____ hours and ____ minutes

Full solution

Q. After spending the winter in Fulton County, two flocks of birds are now migrating home. The first flock flies due east at 3333 kilometers per hour, and the second flies west at 6363 kilometers per hour. In how much time will they be 390390 kilometers apart? If necessary, round your answer to the nearest minute.\newline____ hours and ____ minutes
  1. Calculate Combined Speed: We have:\newlineSpeed of first flock: 3333 kilometers per hour\newlineSpeed of second flock: 6363 kilometers per hour\newlineFind the combined speed of the two flocks since they are flying in opposite directions.\newlineCombined speed = Speed of first flock + Speed of second flock\newlineCombined speed = 33+6333 + 63\newlineCombined speed = 9696 kilometers per hour
  2. Find Time Taken: Now, we need to find the time it takes for them to be 390390 kilometers apart.\newlineUse the formula: Time=DistanceSpeed\text{Time} = \frac{\text{Distance}}{\text{Speed}}\newlineTime=390 kilometers96 kilometers per hour\text{Time} = \frac{390 \text{ kilometers}}{96 \text{ kilometers per hour}}\newlineTime4.0625 hours\text{Time} \approx 4.0625 \text{ hours}
  3. Convert Decimal Hours: To convert the decimal hours to minutes, we take the fractional part and multiply by 6060. \newline0.06250.0625 hours ×60\times 60 minutes/hour 3.75\approx 3.75 minutes \newlineSince we need to round to the nearest minute, we round 3.753.75 minutes to 44 minutes.
  4. Final Result: So, the flocks of birds will be 390390 kilometers apart in approximately 44 hours and 44 minutes.

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