Respuesta :
The 50 mile distance traveled downstream and back that takes 2 hours and 5 hours respectively gives;
- The speed of the boat in still water = 17.5 mph
- The river current flows at 7.5 mph
How can the boat speed be calculated?
Let v represent the speed of the boat and let u represent the speed of the river current.
Distance the boat travels downstream = 50 miles
Time taken to travel downstream by the boat = 2 hours
Time taken to travel back upstream = 5 hours
[tex]velocity = \frac{distance}{time} [/tex]
Therefore;
Which gives;
[tex]v + u = \frac{50}{2} = 25...(1)[/tex]
- v + u = 25
[tex]v - u = \frac{50}{5} = 10...(2)[/tex]
- v - u = 10
Adding equation (1) to equation (2) gives;
(v + u) + (v - u) = 2•v = 25 + 10 = 35
2•v = 35
v = 35 ÷ 2 = 17.5
- The speed of the boat, v = 17.5 mph
u = 25 - v
Which gives;
u = 25 - 17.5 = 7.5
- The speed of the river current, u = 7.5 mph (downstream)
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