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?

A. 2+5=c
B. 2+c=5
C. c-2=5
D. 5-2=c
all the numbers and letter are to the second power

Answer 1

Omyra's error is in setting up the equation to find the distance between Joseph and Isabelle after 1.5 hours. Instead of subtracting their distances, she incorrectly added them together.

Step-by-step explanation:

The correct statement that describes Omyra's error is B. 2+c=5. Omyra made an error in setting up the equation to find c, the distance between Joseph and Isabelle after 1.5 hours. Instead of correctly subtracting the distances traveled by Joseph and Isabelle from the starting point, Omyra incorrectly added them together, which resulted in the incorrect equation 2+c=5. To find the correct equation, we need to consider that Joseph traveled 8 km/h for 1.5 hours north, so his distance is 8 km/h x 1.5 hours = 12 km north.

Isabelle traveled 12 km/h for 1.5 hours west, so her distance is 12 km/h x 1.5 hours = 18 km west. To find the distance between Joseph and Isabelle after 1.5 hours, we need to consider the right-angled triangle formed by their paths. Using the Pythagorean theorem, the distance c can be calculated as c = sqrt(12^2 + 18^2) = sqrt(144 + 324) = sqrt(468) = 6 sqrt(13) km. Therefore, the correct equation is 2 + c = 5.