Flow to opposite of stream flow is resistance full. The speed of the considered boat in still water is 25 miles per hour.
How does stream flow affect the net speed of boat?
If boat goes along the stream flow (downstream), then the speed of boat will be increased as stream will help boat go faster. In contrast, the upstream flow of boat will be slower than its speed in normal flow due to stream resistance.
For the given case, if we assume that the speed of the considered boat in the still water be S miles per hour, then:
As it is given that the current's speed is 5 miles per hour, thus,
- Speed of boat downstream = S + 5 miles per hour
- Speed of boat upstream = S - 5 miles per hour
If we consider the time 't' hours in which the boat traveled the distance 240 miles downstream, and 160 miles upstream, then by using the fact that speed is the ratio of the distance covered to time taken, we get:
[tex]S - 5 = \dfrac{160}{t}\\\\S + 5 = \dfrac{240}{t}[/tex]
Using the first equation to get S in terms of t, we get:
[tex]S - 5 = \dfrac{160}{t}\\\\S = \dfrac{160 + 5t}{t}[/tex]
Substituting this value of S in second equation, we get:
[tex]S + 5 = \dfrac{240}{t}\\\\\dfrac{160 + 5t}{t} + 5 = \dfrac{240}{t}\\\\ 160 + 5t + 5t = 240\\10t = 80\\t = 8[/tex]
The boat took 8 hours to travel 240 miles downstream and 160 miles upstream. Putting this value back in the expression for S, we get:
[tex]S = \dfrac{160 + 5t}{t} = \dfrac{160 + 40}{8} = 25[/tex] (miles per hour)
Thus, the speed of the boat in still water is S = 25 miles per hour.
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