Question

on may 26, 1934, a streamlined, stainless steel diesel train called the zephyr set the worlds nonstop long-distance speed record for trains. its run from denver to chicago took 13 hours, 4 minutes, 58 seconds, and was witnessed by more than a million people along the route. the total distance traveled was 1633.8 km. what was its average speed in km/h? 124.9 km/h what was its average speed in m/s? 34.7 m/s

Explanation:

For average speed in km/h:

Step1: Convert time to hours

First, convert 4 minutes to hours: \( 4\ \text{min} = \frac{4}{60}\ \text{h} \approx 0.0667\ \text{h} \)
Then, convert 58 seconds to hours: \( 58\ \text{s} = \frac{58}{3600}\ \text{h} \approx 0.0161\ \text{h} \)
Total time \( t = 13 + 0.0667 + 0.0161 \approx 13.0828\ \text{h} \)

Step2: Calculate average speed

Average speed \( v = \frac{d}{t} \), where \( d = 1633.8\ \text{km} \) and \( t \approx 13.0828\ \text{h} \)
\( v = \frac{1633.8}{13.0828} \approx 124.9\ \text{km/h} \)

For average speed in m/s:

Step1: Convert distance to meters and time to seconds

Distance \( d = 1633.8\ \text{km} = 1633800\ \text{m} \)
Time: 13 hours = \( 13 \times 3600 = 46800\ \text{s} \), 4 minutes = \( 4 \times 60 = 240\ \text{s} \), so total time \( t = 46800 + 240 + 58 = 47098\ \text{s} \)

Step2: Calculate average speed

Average speed \( v = \frac{d}{t} = \frac{1633800}{47098} \approx 34.7\ \text{m/s} \)

Answer:

(for km/h):
\( \approx 124.9\ \text{km/h} \)