Question

The distance between two stops is \(5\ \text{km}\), the average speed is \(50\ \text{km/h}\), and the stop time is \(2\) minutes. Find the scheduled speed.

• A. \(37.5\ \text{km/h}\)
• B. \(42.5\ \text{km/h}\)
• C. \(30\ \text{km/h}\)
• D. \(50\ \text{km/h}\)

Hint:

Scheduled speed includes stop time, while average speed considers only running time.

Answer 1

The Correct Option is A

Concept: Average speed excludes stop time, while scheduled speed includes stop time. \[ \text{Scheduled speed}=\frac{\text{Distance}}{\text{Running time}+\text{Stop time}} \]

Step 1: Given distance: \[ D=5\ \text{km} \] Average speed: \[ V_a=50\ \text{km/h} \]

Step 2: Running time: \[ t_r=\frac{D}{V_a} \] \[ t_r=\frac{5}{50}\ \text{h} \] \[ t_r=0.1\ \text{h} \] Convert into minutes: \[ 0.1\times60=6\ \text{min} \]

Step 3: Stop time: \[ t_s=2\ \text{min} \] Total scheduled time: \[ t=6+2=8\ \text{min} \] Convert into hours: \[ t=\frac{8}{60}\ \text{h} \]

Step 4: Scheduled speed: \[ V_s=\frac{5}{8/60} \] \[ V_s=5\times\frac{60}{8} \] \[ V_s=37.5\ \text{km/h} \] Therefore: \[ \boxed{37.5\ \text{km/h}} \]