Given:
The current of a river is 2 miles per hour. A boat travels to a point 8 miles upstream and back in 3 hours.
Required:
What is the speed of the boat in still water?
Explanation:
A boat has to travel 8 miles against the current and 8 miles with the current.
Ustream(against the current) the boat's speed is:
speed in still water - current OR x - 2.
Downstream( with the current) the speed is:
speed in still water + current speed OR x + 2.
We know the distance
[tex]=rate\times time[/tex]OR
[tex]time=\frac{distance}{rate}[/tex]The total time is 3 hours
The time upstream + The time downstream = 3 hours
[tex]\begin{gathered} \frac{distance\text{ }up}{rate\text{ }up}+\frac{the\text{ }distance\text{ }down}{rate\text{ }down}=3\text{ }hours \\ \frac{8}{x-2}+\frac{8}{x+2}=3 \\ \text{ we get,} \\ 3x^2-16x-12=0 \\ x=6,-\frac{2}{3} \end{gathered}[/tex]Answer:
[tex]\text{ The speed of boat in still water is }6\text{ miles per hour.}[/tex]