A cruise boat traveled 72 miles downstream, with the current, in 2 hours. The return trip upstrea., against the current, covered the same distance but tool 6 hours. Find the average velocity of the current.
Let the current have speed c and the boat have speed b. Then,
since time = distance/speed, you have
72/(b+c) = 2
72/(b-c) = 6
Now just solve for c.
To find the average velocity of the current, we need to use the formula:
Average Velocity = (Total Distance) / (Total Time)
In this problem, the total distance covered downstream and upstream is the same, i.e., 72 miles.
Now, let's find the total time taken for the entire trip. We know that downstream, the boat traveled for 2 hours, and upstream, it took 6 hours. Thus, the total time is 2 hours + 6 hours = 8 hours.
Plugging the values into the formula:
Average Velocity = 72 miles / 8 hours
Therefore, the average velocity of the current is 9 miles per hour.
So, the answer is that the average velocity of the current is 9 miles per hour.