Discussion
A man travelling 900 km by train at an average speed of 60 km per hour and 3000 km by boat at an average speed of 25 km/hr. What is the average speed of a man for the entire distance ?
Answer: D
The average speed is 28.88 km per hour.
Average speed is total distance over total time, not the average of the two speeds:
\[ \begin{aligned} t_{\text{train}} &= 900/60 = 15\ \text{h} \\ t_{\text{boat}} &= 3000/25 = 120\ \text{h} \\ \bar{v} &= \frac{3900}{135} = 28.89\ \text{km/h} \end{aligned} \]
The paper prints 28.88, the value cut off after two decimal places. The plain average of the two speeds, 42.5 km/h, is not offered because it ignores that the man spends far longer on the slow boat. The other three options are simply off by whole numbers.
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