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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. How long is the junior varsity team's course?


Hint: Use the Pythagorean Theorem.


7 miles

5 miles

3 miles

Verified Answer :

anthonysilby1

3:4:5 triangle, The junior varsity team's course is 5 miles

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, \(Hypotenuse^2=Perpendicular^2+Base^2\)

\(AC^2=AB^2+BC^2\)

\(x^2=(x-1)^2+3^2\)

\(x^2=x^2+1-2x+3^2\)

\(0=-2x+10\)

\(2x=10\)

\(x=\frac{10}{2}\)

\(x=5\)

Thus the junior varsity team's course is 5 miles long.

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