Firefighter Practice Exam

If Greg drives home from fire academy training at 58 mph and returns at 53 mph, taking an additional 30 minutes, how long is his commute?

1. 261 miles

2. 292.5 miles

3. 301.7 miles

4. 307.4 miles

The correct answer is: 307.4 miles

To determine the length of Greg's commute, we can use the relationship between distance, speed, and time. The total distance he travels is the same for both trips, so we denote the distance as \(d\). First, we can express the time taken for each trip. The time for the commute to the academy at 58 mph can be calculated as \( \frac{d}{58} \), and the return trip at 53 mph can be calculated as \( \frac{d}{53} \). The problem states that the return trip takes an additional 30 minutes (or 0.5 hours) compared to the trip to the academy. Therefore, we can set up the equation: \[ \frac{d}{53} = \frac{d}{58} + 0.5 \] To eliminate the fractions, we can first find a common denominator, which will facilitate solving for \(d\). The lowest common multiple of 53 and 58 is 3074, so we can multiply through by this to clear the denominators: \[ 3074 \left(\frac{d}{53}\right) = 3074\left(\frac{d}{58} + 0.5