Discussion
A man travels the first 2 hours at a speed of 45 km/h, the next \(3\frac{1}{2}\) hours at a speed of 60 km/h and the next \(4\frac{1}{2}\) hours at a speed of 70 km/h. What is his average speed (in km/h) for the entire journey?
Answer: B
The average speed is 61.5 km/h. Average speed is total distance over total time. \[ 2\times 45 = 90\text{ km} \] \[ 3\tfrac{1}{2}\times 60 = 210\text{ km} \] \[ 4\tfrac{1}{2}\times 70 = 315\text{ km} \] \[ \begin{aligned} \text{Distance} &= 615\text{ km},\quad \text{Time} \\ &= 2 + 3.5 + 4.5 \\ &= 10\text{ h} \end{aligned} \] \[ \frac{615}{10} = 61.5\text{ km/h} \] Taking the plain average of 45, 60 and 70 (about 58.3) ignores the different times and does not give any option; 60.5, 62 and 63 do not match the weighted value.
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