Question

The measured spot speeds (in km/h) of 10 vehicles from a traffic stream are 45, 35, 25, 51, 45, 38, 61, 42, 47, and 49. The Time Mean Speed of the traffic stream (in km/h, rounded off to one decimal place) is \(\underline{\hspace{2cm}}\).

Hint:

Time Mean Speed is always the simple average of spot speeds, unlike Space Mean Speed which uses the harmonic mean.

Answer 1

Correct Answer: 43 - 44

The Time Mean Speed (TMS) is defined as the simple arithmetic mean of the spot speeds:
\[ V_t = \frac{\sum v_i}{n} \] Given speeds:
45, 35, 25, 51, 45, 38, 61, 42, 47, 49
Sum of speeds:
\[ 45 + 35 + 25 + 51 + 45 + 38 + 61 + 42 + 47 + 49 = 438 \] Number of vehicles: \(n = 10\).
Thus,
\[ V_t = \frac{438}{10} = 43.8\ \text{km/h} \] Final rounded value (one decimal place):
\[ \boxed{43.8\ \text{km/h}} \]