Question

Joseph and Isabelle left Omyra’s house at the same time. Joseph jogged north at 8 kilometers per hour, while Isabelle rode her bike west at 12 kilometers per hour. Omyra tried to figure out how far apart they were after 1.5 hours. Her work is shown below. Which statements describe her errors? Check all that apply.

She did not find the full distance each traveled in 1.5 hours. She should have used 12 km for Joseph’s distance and 18 km for Isabelle’s distance. She did not square the 12 in the problem. She should have used 12^2=144

She did not evaluate 88  correctly. She should have used 8^2=8(2)=16 She did not evaluate  correctly. She should have used .88=44 She should not have taken the square root of each side when solving. She should have just divided each side by 2. She should not have added the squares in the first step. She should have used .12^2-8^2=d^2

Answer 1

A and B
A because what Omyra found is the distance for an hour and what she wants to find is the distance for an hour and a half.
B because the pythagorean theorem is a^2+b^2=c^2 regardless of whether 12 is A or B... The legs of an triangle should always be squared(before being added of course).
I got it correct on my topic test FYI

Answer 2

For this case the distance will be given by:
d ^ 2 = (12 * 1.5) ^ 2 + (8 * 1.5) ^ 2
Rewriting we have:
d ^ 2 = (18) ^ 2 + (12) ^ 2
d ^ 2 = 324 + 144
d ^ 2 = 468
d = root (468)
d = 21.63 Km
Answer:
1) She did not find the full distance each traveled in 1.5 hours.
2) She should have used 12 km for Joseph's distance and 18 km for Isabelle's distance.