Respuesta :
Answer:
The speed of the current is 7 miles per hour.
Step-by-step explanation:
Let x represent speed of the current.
We have been given that a motorboat maintained a constant speed of 11 miles per hour relative to the water in going 18 miles upstream and then returning.
The speed of motorboat while going upstream would be [tex]11-x[/tex].
The speed of motorboat while going downstream would be [tex]11+x[/tex].
[tex]\text{Time}=\frac{\text{Distance}}{\text{Speed}}[/tex]
Time taken while going upstream would be [tex]\frac{18}{11-x}[/tex].
Time taken while going downstream would be [tex]\frac{18}{11+x}[/tex].
Now we will compare sum of both times with total time 5.5 hours and solve for x as:
[tex]\frac{18}{11-x}+\frac{18}{11+x}=5.5[/tex]
[tex]\frac{18(11+x)}{(11-x)(11+x)}+\frac{18(11-x)}{(11-x)(11+x)}=5.5(11-x)(11+x)[/tex]
[tex]198+18x+198-18x=5.5(11-x)(11+x)[/tex]
[tex]396=5.5(121-x^2)[/tex]
[tex]396=665.5-5.5x^2[/tex]
[tex]665.5-5.5x^2=396[/tex]
[tex]665.5-665.5-5.5x^2=396-665.5[/tex]
[tex]-5.5x^2=-269.5[/tex]
[tex]\frac{-5.5x^2}{-5.5}=\frac{-269.5}{-5.5}[/tex]
[tex]x^2=49[/tex]
Take positive square root of both sides:
[tex]\sqrt{x^2}=\sqrt{49}[/tex]
[tex]x=7[/tex]
Therefore, the speed of the current is 7 miles per hour.
