Question

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

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

4. How much farther does Jane travel than her trainer?

Answer 1

Part 1. 28 miles

Part 2. 16^2 + 12^2 = c^2

Part 3. 8 miles. All work is in step by step explanation.

Part 4. 8 miles

Explanation:

Part 1. The total distance that Jane travels biking and running is 28 miles. This is because we add 16 and 12 which is her total route.

Part 2. The Pythagorean theorem is a^2 + b^2 = c ^2. In this case, the variable a is Jane's bike route(16 miles), the variable b is Jane's running route(12 miles), and the variable c is the Trainer's biking route as given. If we replace all variables with the values in miles, the equation would be 16^2 + 12^2 = c^2.

Part 3. WORK USED FROM EQUATION

16^2 = 16*16 = 256

12^2 = 12*12 = 144

Now we replace the numbers with the exponents with the solved numbers.

256 + 144 = c^2

256 + 144 = 400

400 = c^2

c = sqrt400

c = 20

Finally, we take the value of c and subtract it from the total distance of Jane's route which is 28 miles(as explained above).

28 - 20 = 8.

Hence, the answer is 8 miles