Question

Select all the correct answers.

Alan needs to drive 400 miles to reach Madison. He is driving at a constant speed of 55 miles per hour. The function y = 400 − 55x represents Alan’s distance in miles from Madison in terms of the number of hours he drives. Andrew is also driving at a constant speed to reach Madison. The table represents Andrew’s distance in miles from Madison in terms of the number of hours he drives.


x y
1 323
3 209

Which statements about this situation are true?
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I REPEAT PICK MORE THAN ONE ANSWER!!!

Alan is driving at a faster speed.

Andrew is driving at a faster speed.

Alan and Andrew are driving at the same speed.

Alan was farther away from Madison when he started driving.

Andrew was farther away from Madison when he started driving.

Alan and Andrew started the same distance from Madison.

Answer 1

Answer: Let’s analyze the given information:Alan is driving at a constant speed of 55 miles per hour. The function y = 400 − 55x represents Alan’s distance in miles from Madison in terms of the number of hours he drives. This means Alan started 400 miles away from Madison.For Andrew, we have two data points: (1, 323) and (3, 209). This means after 1 hour, Andrew was 323 miles away, and after 3 hours, he was 209 miles away. So, in 2 hours (from hour 1 to hour 3), Andrew covered a distance of 323 - 209 = 114 miles. Therefore, Andrew’s speed is 114 miles / 2 hours = 57 miles per hour. This means Andrew started 323 miles away from Madison.Based on this analysis, the following statements are true:Andrew is driving at a faster speed. (Andrew’s speed is 57 mph while Alan’s speed is 55 mph)Alan was farther away from Madison when he started driving. (Alan started 400 miles away while Andrew started 323 miles away)

Explanation:

Answer 2

Andrew is driving at a faster speed and they both started at the same place.