Question

I need help with this practice. Assistance would be greatly appreciated.

Jane is training for a triathlon. After swimming a few laps, she leaves the health club and bikes 16 miles south. She then runs 12 miles west. Her trainer bikes from the health club to meet Jane at the end of her run.




How much farther does Jane travel than her trainer? Answer the questions to find out.



1. What is the total distance Jane travels biking and running? Include units with your answer. (2 points)









2. Use the Pythagorean theorem to write an equation for the distance Jane's trainer bikes. (2 points)





3. Solve your equation to find the distance Jane's trainer bikes. Show your work. (3 points)



4. How much farther does Jane travel than her trainer? (3 points)

Answer 1

1 The total distance Jane travels biking and running is the hypotenuse of a right triangle with legs 16 miles and 12 miles. Using the Pythagorean theorem, we can find this distance:

distance = sqrt(16^2 + 12^2) = sqrt(256 + 144) = sqrt(400) = 20 miles

So Jane travels a total of 20 miles.

2 The distance Jane's trainer bikes is the distance from the health club to the point where he meets Jane. Let's call this distance x. We can represent this with the following right triangle:

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A (health club)

|

|

| x

|

|

B (meeting point)

where A and B are points on a coordinate plane, and the x-axis represents the direction Jane runs.

Using the Pythagorean theorem, we can write:

x^2 + 12^2 = d^2

where d is the distance from the health club to the end of Jane's run. We know that d = 20, so we can substitute:

x^2 + 12^2 = 20^2

3. Solving for x:

x^2 + 144 = 400

x^2 = 256

x = sqrt(256) = 16

So Jane's trainer bikes 16 miles.

4 Jane travels 20 - 16 = 4 miles farther than her trainer.

Explanation: