Answer:
[tex]x=1824218 ft [/tex]
Step-by-step explanation:
The figure attached show a general description of the problem.
For this case the best way to solve the problem is use the general equation for an hyperbola given by:
[tex]\frac{y^2}{a^2} -\frac{x^2}{b^2}=1[/tex]
We assume that the longer axis for the hyperbola is on the y axis.
On this case the total distance traveled by the sound is 1100 and we can find the value of a like this:
[tex]2a = 1100[/tex]
[tex]a =\frac{1100}{2}=550[/tex]
Since both people are apart 6 miles we can find the value of c like this:
[tex] 2c =2(6)[/tex]
c= 6 miles and we can convert this into ft like this:
[tex] 6miles *\frac{5280ft}{1 mile}=31680ft[/tex]
And we can find the value of b like this:
[tex] b^2 = c^2 -a^2 = (31680)^2 -(550)^2=1003319900[/tex]
And then our equation is given by:
[tex]\frac{y^2}{302500} -\frac{x^2}{1003319900}=1[/tex]
And for this case we want to find the value of x when y = 6ft=31680 ft[/tex], and solving for x we got:
[tex]\frac{31680^2}{302500} -\frac{x^2}{1003319900}=1[/tex]
[tex]\frac{x^2}{1003319900} = \frac{31680^2}{302500} -1[/tex]
[tex]x=1824218 ft [/tex]
