Answer: [tex]1.8\ mph[/tex]
Step-by-step explanation:
Let be "x" the speed of current (in mph).
According to the exercise, we know that the speed of the steamer in still water is 18 mph, so its speed downstream with the water current is:
[tex]18 +x[/tex]
Since going downstream it convered the distance between the two ports in 3 hours, then distance is:
[tex]d=3(18 +x)[/tex] [Equation 1]
The speed upstream in mph can be represetend with:
[tex]18-x[/tex]
You know that the return trip took 3 hours 40 minutes. Since there are 60 minutes in 1 hour, this time is:
[tex](3+\frac{2}{3})hours=\frac{11}{3}hours[/tex]
Therefore, the distance travelled upstream is:
[tex]d=\frac{11}{3}(18-x)[/tex] [Equation 2]
Make [tex][Equation 1]=[Equation 2][/tex] and solve for "x":
[tex]3(18 +x)=\frac{11}{3}(18-x)\\\\54+3x=66-\frac{11}{3}x\\\\3x+\frac{11}{3}x=66-54\\\\\frac{20}{3}x=12\\\\x=(\frac{3}{20})(12)\\\\x=1.8[/tex]
