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A twig floats downstream at a rate of 44 kilometers per hour. At the same time, 22 kilometers downstream, a trout begins swimming upstream, moving toward the twig at 1616 kilometers per hour. In how much time will the fish swim by the twig?\newlineIf necessary, round your answer to the nearest minute.\newline____ hours and ____ minutes\newline

Full solution

Q. A twig floats downstream at a rate of 44 kilometers per hour. At the same time, 22 kilometers downstream, a trout begins swimming upstream, moving toward the twig at 1616 kilometers per hour. In how much time will the fish swim by the twig?\newlineIf necessary, round your answer to the nearest minute.\newline____ hours and ____ minutes\newline
  1. Calculate Relative Speed: We need to calculate the relative speed of the trout to the twig. Since the trout is swimming upstream and the twig is floating downstream, we add their speeds to find the relative speed at which they are approaching each other.\newlineRelative speed =Speed of trout+Speed of twig= \text{Speed of trout} + \text{Speed of twig}\newlineRelative speed =16km/h+4km/h= 16 \, \text{km/h} + 4 \, \text{km/h}\newlineRelative speed =20km/h= 20 \, \text{km/h}
  2. Find Time Taken: Now we need to find the time it takes for the trout to swim 22 kilometers at the relative speed of 2020 kilometers per hour.\newlineTime = Distance / Relative speed\newlineTime = 2km/20km/h2 \, \text{km} / 20 \, \text{km/h}\newlineTime = 0.10.1 hours
  3. Convert Time to Minutes: To convert the time from hours to minutes, we multiply by 6060 minutes per hour.\newlineTime in minutes = Time in hours ×60\times 60 minutes/hour\newlineTime in minutes = 0.10.1 hours ×60\times 60 minutes/hour\newlineTime in minutes = 66 minutes

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