Question

select the correct answer. danny is taking a road trip. after 36 miles, he reaches a stretch of highway with a speed limit of 60 miles/hour. danny is trying to figure out the minimum number of hours hell need to drive to reach over 300 total miles for the trip, assuming he stays under or at the speed limit. he creates the inequality 60t + 36 ≥ 300, where t is the time elapsed, in hours. what statement is the most accurate? a. danny needs at least 7 hours to drive 300 miles. b. danny may drive 300 miles in 5 hours. c. at 4 hours, danny will have just driven 300 miles. d. it isnt possible to drive 300 miles before the day is over.

Explanation:

Step1: Analyze the inequality meaning

The inequality \(60t + 36\geq300\) represents the situation where Danny has already driven 36 miles and then drives at a speed of 60 miles per - hour for \(t\) hours, and the total distance should be at least 300 miles. Solving for \(t\) gives \(60t\geq300 - 36\), then \(60t\geq264\), and \(t\geq4.4\) hours. The total time to drive 300 miles or more is the sum of the time after the first 36 - mile stretch and any time before that.

Step2: Evaluate each option

• Option A: Danny needs at least 7 hours to drive 300 miles. There is no evidence in the inequality that he needs at least 7 hours.
• Option B: Danny may drive 300 miles in 5 hours. If \(t = 5\), then \(60t+36=60\times5 + 36=300 + 36=336\) miles. But the inequality is about the minimum time needed to reach over 300 miles, and we found \(t\geq4.4\) hours, and this option doesn't accurately represent the meaning of the inequality.
• Option C: At 4 hours, Danny will have just driven 300 miles. If \(t = 4\), then \(60t+36=60\times4+36=240 + 36=276

eq300\).

• Option D: It isn't possible to drive 300 miles before the day is over. There is no information about the time - limit of the day in the problem, but the inequality \(60t + 36\geq300\) is mainly about the relationship between time, speed, and distance. The most accurate statement related to the inequality is that Danny needs to drive for a certain minimum number of hours to reach over 300 miles. The inequality \(60t+36\geq300\) implies that he needs to drive for enough time \(t\) such that the total distance is at least 300 miles. Since \(60t+36\geq300\) gives \(t\geq4.4\) hours in addition to any time before the first 36 - mile stretch, the statement that is most in line with the inequality is that Danny needs at least a certain amount of time to drive 300 miles. The inequality \(60t + 36\geq300\) is based on the fact that he has already driven 36 miles and then drives at 60 miles per hour for \(t\) hours to reach 300 miles or more.

Answer:

A