The travel times of three vehicles on a 2 km stretch of road are 4, 5, and 8 minutes. Assuming the speed of each vehicle to be constant in this stretch, the Space Mean Speed (in km/h) of the vehicles is ________ (rounded off to two decimal places).

The correct answer is 21.18.

Space mean speed is defined as the harmonic mean of the speeds of the vehicles, which is equivalent to the total distance traversed by all the vehicles divided by the total time taken by them to traverse that distance.

The formula for Space Mean Speed ($V_s$) is given by:

$$V_s=\frac{n\times d}{\sum _{i=1}^n{t}_i}$$

Where:
• $n$ is the number of vehicles (3 in this case)
• $d$ is the length of the road stretch (2 km)
• $t_i$ is the travel time of the $i$-th vehicle in hours.

First, we calculate the sum of the travel times of all three vehicles in minutes:

$\sum t_i=4+5+8=17\text{minutes}$

Next, we convert this total travel time from minutes to hours:

$\text{Total Time in hours}=\frac{17}{60}\text{hours}$

Now, we calculate the total distance traveled by all three vehicles over the 2 km stretch:

$\text{Total Distance}=3\times 2=6\text{km}$

Finally, we apply these values to the Space Mean Speed formula:

$V_s=\frac{6}{\left(\frac{17}{60}\right)}$

Simplifying the fraction gives:

$V_s=\frac{6\times 60}{17}=\frac{360}{17}\approx 21.176\text{km/h}$

Rounding off to two decimal places, the Space Mean Speed of the vehicles is 21.18 km/h.