Multiple choice

During a workday, two drivers leave the same depot. Mike departs at 7:00 a.m. and travels north at a constant speed of 36 miles per hour. Sara leaves the depot at 9:00 a.m. and travels south at a constant speed of 24 miles per hour. At some time after 9:00 a.m., a dispatcher checks the tracker and finds that the total distance traveled by Mike and Sara combined is 252 miles. At what time did the dispatcher check the tracker?

  1. 11:00 a.m.

  2. 12:00 p.m.

  3. 1:00 p.m.

  4. 1:30 p.m.

  5. 2:00 p.m.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let t be the time in hours after 9:00 a.m. Mike has traveled for t+2 hours. Distance = 36(t+2) + 24t = 252. 36t + 72 + 24t = 252 => 60t = 180 => t = 3. 9:00 a.m. + 3 hours = 12:00 p.m.

AI explanation

From 7:00 a.m. to 9:00 a.m., Mike travels alone for 2 hours, covering 36 * 2 = 72 miles. After 9:00 a.m., their combined speed using relative speed concepts is 36 + 24 = 60 miles per hour. To cover the remaining 180 miles of the 252 mile total, they need 180 / 60 = 3 hours, meaning the dispatcher checked the tracker at 12:00 p.m.

Keep practicing — related questions