Answer:
The speed of the current is 5 miles per hour.
Step-by-step explanation:
Given, Joy kayaked up the river and then back in a total time of 6 hours.
The trip was 4 miles each way.
The current was difficult.
Let the speed of current be 'a' miles per hour
If joy kayaked at a speed of 5 mph in still water, we have to find what is the speed of the current?
Now, we know that,
distance = speed x time
So,
[tex]time =\frac{ Distance}{speed}[/tex]
Then, total time = time for up stream + time for down stream
[tex]6 hours = \frac{(4 miles)}{(a-\text{5 miles per hours})} +\frac{ (4 miles)}{(a+\text{5 miles per hour})}[/tex]
[tex]6 = \frac{4}{(a-5)}+ \frac{4}{(a+5)}[/tex]
[tex]\frac{ 6}{4}= \frac{ 1}{(a-5)}+ \frac{ 1}{(a+5)}[/tex]
[tex]\frac{3}{2}= \frac{ (a+5+a-5)}{((a-5)(a+5))}[/tex]
[tex]\frac{ 3}{2}= \frac{ 2a}{(a^2- 5^2 )}[/tex]
[tex]3(a^2- 25) = 4a[/tex]
[tex]3a^2 -4a -75 = 0[/tex]
Now, let us use quadratic formula,[tex]x =\frac{ (-b\pm\sqrt{(b^2-4ac)})}{2a}[/tex] to find a value.
Then,[tex]a = \frac{(-(-4)\pm\sqrt{(-4)^2-(4 \times 3 \times(-75)})}{(2 \times 3)}[/tex]
[tex]A = \frac{(4\pm\sqrt{(16+ 12 x 75))}}{6}[/tex]
[tex]A =\frac{ (4\pm\sqrt{916}}{6}[/tex]
[tex]A =\frac{ (4 \pm 30.265)}{6}[/tex]
[tex]A =\frac{ 34.2656}{6}[/tex]
we can neglect – ve values of speed.
A = 5.71
