Answer:
5 miles
Step-by-step explanation:
We are given that A varsity cross-country team runs on a course that makes a right turn after 3 miles, and continues on one mile less than the junior varsity team's course.
The junior varsity team's course runs on a straight line from the same starting point and the finish line.
Refer the attached figure
Let the junior runs course x miles i.e. AC = x
Senior runs 3 miles i.e. BC = 3 miles
Senior continues on one mile less than the junior ie. AB = x-1
Since ΔABC is a right angles triangle
So, [tex]Hypotenuse^2=Perpendicular^2+Base^2[/tex]
[tex]AC^2=AB^2+BC^2[/tex]
[tex]x^2=(x-1)^2+3^2[/tex]
[tex]x^2=x^2+1-2x+3^2[/tex]
[tex]0=-2x+10[/tex]
[tex]2x=10[/tex]
[tex]x=\frac{10}{2}[/tex]
[tex]x=5[/tex]
Thus the junior varsity team's course is 5 miles long.
