Respuesta :
The average speed of the river's current is 1.49107 miles per hour
Solution:
Given that,
Upstream distance = 4 miles
Downstream distance = 4 miles
If the speed of a boat in still water is u km\hr and the speed of the stream is v km/hr then:
Speed downstream = u + v km\hr
Speed upstream = u - v km\hr
From given,
Speed in still water = 2.3 miles per hour
u = 2.3
Therefore,
speed downstream = 2.3 + v
Speed upstream = 2.3 - v
The total time is 6 hours
Therefore,
[tex]time = \frac{distance}{speed}[/tex]
Thus we get,
[tex]\frac{4}{2.3+v}+\frac{4}{2.3-v} = 6\\\\4(\frac{1}{2.3+v} + \frac{1}{2.3-v}) = 6\\\\\frac{1}{2.3+v} + \frac{1}{2.3-v} = \frac{6}{4}\\\\\frac{2.3 - v + 2.3 + v }{2.3^2 - v^2} = \frac{6}{4}\\\\\frac{4.6}{5.29-v^2} = \frac{6}{4}\\\\31.74 - 6v^2 = 18.4\\\\6v^2 = 13.34\\\\v^2 = 2.2233\\\\v = 1.49107[/tex]
Thus the average speed of the river's current is 1.49107 miles per hour
