Solve the problem.
-Two airplanes leave an airport at the same time, one going northwest $$\text { (bearing } 135 ^ { \circ } \text { ) }$$ at 415 mph and the other going east at 329 mph. How far apart are the planes after 2 hours (to the nearest
Mile)?
A) 1228 mi
B) 688 mi
C) 1376 mi
D) 1147 mi

Question

Quizplus · Accepted Answer

After 2 hours, the plane going northwest at 415 mph will have traveled a distance of $415 \times 2 = 830$ miles, and the plane going east at 329 mph will have traveled $329 \times 2 = 658$ miles. To find the distance between the two planes, we can use the Pythagorean theorem, since the planes' paths form a right-angled triangle with the legs being 830 miles and 658 miles. The distance between the planes is $\sqrt{830^2 + 658^2} \approx 1061.7$ miles, which is not an option provided. However, the bearing of 135 degrees indicates a direction southwest (not northwest as stated), which would mean the calculation approach based on the given options and scenario seems to have a discrepancy. Given the options and assuming a correct interpretation of the bearing as southeast (135 degrees from north), or considering a typo in the direction, recalculating with the correct understanding of bearings or assuming a typo in the question's direction details, none of the provided distances match the calculated 1061.7 miles based on the initial interpretation. Re-evaluating the scenario with the correct application of bearings or considering potential misinterpretations, and ensuring the calculation aligns with standard navigational bearings, it's crucial to correctly apply the bearing and speed information. However, without adjusting for the apparent discrepancy in the bearing direction, the calculation provided does not directly lead to one of the given answers, indicating a need to reassess the bearing interpretation or a mistake in the initial problem setup or calculation.Given the nature of the problem and the options provided, without a clear path to one of the given answers based on the initial calculation and bearing interpretation, and acknowledging a potential misunderstanding in the bearing direction or a typo in the question, the correct response based on the standard approach to such a problem cannot be confidently determined without further clarification or correction of the bearing direction.

Solve the Problem (bearing 135∘ ) \text { (bearing } 135 ^ { \circ } \text { ) } (bearing 135∘ )

Solve the Problem $\text { (bearing } 135 ^ { \circ } \text { ) }$