How Fire Inspector Meetings Work Under the Clock

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.?

• A. 9:15 a.m.
• B. 10:00 a.m.
• C. 10:20 a.m.
• D. 1:15 p.m.

Answer: (B)

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.

Understanding the nuances of speed, distance, and time can seem daunting, but it’s a crucial skill for aspiring firefighters—especially when taking the firefighter examination. Let’s break it down with a relatable example that illustrates how these concepts are applied practically.

Imagine two fire inspection officers setting off from different towns, heading toward each other. One's cruising at 57 mph while the other’s speeding along at 68 mph. They’re starting from cities that are 469 miles apart, and they've decided to embark on this journey at 6:15 a.m. If you were in their shoes, wouldn't you want to know when you'd cross paths?

To find out when they'll meet, we first need to figure out how quickly they’re closing the gap. It’s all about teamwork and speed here! By adding their velocities—57 mph + 68 mph—we get a combined speed of 125 mph. Now, why does this matter? Simple. The faster they close the distance, the sooner they meet, right?

Next up, it’s time for some math magic! We divide the total distance of 469 miles by their harmonious speed of 125 mph. Doing the math reveals it’ll take them 3.752 hours, which rounds up to about 3 hours and 45 minutes. But hang on—what does that mean in real-world terms?

If they set off at 6:15 a.m., adding 3 hours brings us to 9:15 a.m. Now you just need to sprinkle in those 45 minutes, and voilà! They’ll cross paths at 10:00 a.m. Isn't that neat?

This calculation not only tells you the exact time of their meeting but emphasizes the importance of these mathematical principles in fire inspection scenarios. Learning to connect speed, distance, and time enables firefighters and inspectors to make timely decisions, which can be critical in emergency situations.

So the next time you see numbers flying on a firefighter exam, remember the officers on their journey, meeting under the clock. Armed with the knowledge of how to calculate these distances and times, you’ll surely rise to the occasion during your examination!