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.
A right triangle. The distance north from Omyra's House is 8 kilometers, and the distance west is 12 kilometers.

8 squared + 12 squared = d squared. 64 + 24 = d squared. 88 = d squared. StartRoot 88 EndRoot = d. 9.4 almost-equals d.
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 squared = 144.
She did not evaluate 8 squared correctly. She should have used 8 squared = 8 (2) = 16.
She did not evaluate StartRoot 88 EndRoot correctly. She should have used StartRoot 88 EndRoot almost-equals 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 squared minus 8 squared = d squared.

Answer 1

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.