Question

On May 26, 1934, a streamlined, stainless steel diesel train called the Zephyr set the world’s nonstop long-distance speed record for trains. Its run from Denver to Chicago took $\mathbf{13}\mathbf{hours},\mathbf{4}\mathbf{minutes},\mathbf{58}\mathbf{seconds}$ , and was witnessed by more than a million people along the route. The total distance travelled was $\mathbf{1633}.\mathbf{8}\mathbf{km}$. What was its average speed in km/hand m/s?

Short answer

$\mathbf{124}\mathbf{.}\mathbf{88}\mathbf{\text{\hspace{0.17em}km/h}}$ and $\mathbf{34}\mathbf{.}\mathbf{689}\mathbf{\text{\hspace{0.17em}m/s}}$

Step-by-step solution

Given Data

• Distance $=\mathbf{1633}.\mathbf{8}\mathbf{km}=\mathbf{1633800}\mathbf{m}$.

• Time is taken in hours= $\mathbf{13}\mathbf{h}\mathbf{+}\mathbf{4}\mathbf{min}\mathbf{+}\mathbf{58}\mathbf{\text{\hspace{0.17em}s}}\mathbf{=}\mathbf{13}\mathbf{h}\mathbf{+}\frac{\mathbf{4}}{\mathbf{60}}\mathbf{h}\mathbf{+}\frac{\mathbf{58}}{\mathbf{3600}}\mathbf{h}\mathbf{=}\mathbf{13}\mathbf{+}\mathbf{0}\mathbf{.066}\mathbf{+}\mathbf{0}\mathbf{.01611}\mathbf{=}\mathbf{13}\mathbf{.0821}\mathbf{h}$
• Time is taken in seconds = $\mathbf{=}\mathbf{13}\mathbf{\times }\mathbf{3600}\mathit{s}\mathbf{+}\mathbf{4}\mathbf{\times }\mathbf{60}\mathit{s}\mathbf{+}\mathbf{58}\mathit{s}\mathbf{=}\mathbf{46800}\mathbf{+}\mathbf{240}\mathbf{+}\mathbf{58}\mathbf{=}\mathbf{47098}\mathit{s}$ .

Average speed

If the distance covered is d in time t, then the speed can be calculated as:

$\mathrm{Speed}=\frac{\mathrm{d}}{\mathrm{t}}$

The speed covered in km/h can be calculated as:

$\begin{array}{c}\mathrm{Speed}=\frac{1633.8\text{\hspace{0.17em}km}}{13.0821\text{\hspace{0.17em}h}}\\ =124.88\text{\hspace{0.17em}km/h}\end{array}$

The speed covered in m/s can be calculated as:

$\begin{array}{c}\mathrm{Speed}=\frac{1633800\text{\hspace{0.17em}m}}{47098\text{\hspace{0.17em}s}}\\ =34.689\text{\hspace{0.17em}m/s}\end{array}$

Therefore, the speed is $\mathbf{124}\mathbf{.}\mathbf{88}\mathbf{\text{\hspace{0.17em}km/h}}$and$\mathbf{34}\mathbf{.}\mathbf{689}\mathbf{\text{\hspace{0.17em}m/s}}$ .