Firefighter Practice Exam

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Two fire inspection officers traveling towards each other at rates of 57 mph and 68 mph will pass each other after starting from cities 469 miles apart. What time will they meet if they departed at 6:15 a.m.?

9:15 a.m.
10:00 a.m.
10:20 a.m.
1:15 p.m.

The correct answer is: 10:00 a.m.

To find out when the two fire inspection officers will meet, it's important to first determine the time it takes for them to cover the distance between them. The total rate at which they are closing the distance between each other is the sum of their speeds: 57 mph + 68 mph, which equals 125 mph. Next, we divide the total distance of 469 miles by their combined speed of 125 mph to find the time taken to meet. 469 miles ÷ 125 mph = 3.752 hours, or approximately 3 hours and 45 minutes. Now, if they departed at 6:15 a.m., we need to add 3 hours and 45 minutes to that time. Starting from 6:15 a.m., adding 3 hours results in 9:15 a.m. Then, adding the remaining 45 minutes brings the time to 10:00 a.m. Therefore, the correct answer, indicating the time at which the two officers will meet, is 10:00 a.m. This calculation not only provides the time of their meeting but also highlights the importance of understanding speed, time, and distance relationships in problem-solving.