Respuesta :
Answer:
Average rowing velocity of boat in still water is 4 miles per hour and average velocity of the current is 1 mile per hour.
Step-by-step explanation:
We are given the following in the question:
Let x be the average rowing velocity of boat in still water and y be the the average velocity of the current.
[tex]\text{Speed} = \displaystyle\frac{\text{Distance}}{\texr{Time}}[/tex]
The boat rowed 7.5 miles downstream, with the current, in 1.5 hours.
Velocity with the current =
[tex]=\text{average rowing velocity of boat in still water} + \text{ average velocity of the current} = x + y[/tex]
Thus, we can write the equation:
[tex]7.5 = (x+y)1.5\\x+y = 5[/tex]
The return trip upstream, against the current, covered the same distance, but took 2.5 hours.
Velocity against the current =
[tex]=\text{average rowing velocity of boat in still water} - \text{ average velocity of the current} = x - y[/tex]
Thus, we can write the equation:
[tex]7.5 = (x-y)2.5\\x-y = 3[/tex]
Solving, the two equations:
[tex]2x = 8\\x = 4, y = 1[/tex]
Thus, average rowing velocity of boat in still water is 4 miles per hour and average velocity of the current is 1 mile per hour.
