Calculating Weighted Average: Analyzing Roller Coaster Speeds

A company is making an advertisement for a new roller coaster and they want to know what the weighted average of its travel speed is.



What is the average speed of the roller coaster?

To solve this problem, we'll compute the weighted average speed of the roller coaster using the given weights and speeds:

• Step 1: Convert the weights from percentages to decimal form:

  • 20% becomes 0.20

  • 15% becomes 0.15

  • 5% becomes 0.05

  • 35% becomes 0.35

  • 5% becomes 0.05

  • 20% becomes 0.20

• Step 2: Calculate each term by multiplying the speed by its corresponding weight:

• $\begin{aligned} 100 \times 0.20 &= 20, \\ 40 \times 0.15 &= 6, \\ 130 \times 0.05 &= 6.5, \\ 60 \times 0.35 &= 21, \\ 15 \times 0.05 &= 0.75, \\ 75 \times 0.20 &= 15. \end{aligned}$

• Step 3: Sum the results of these products:

• $20 + 6 + 6.5 + 21 + 0.75 + 15 = 69.25$

• Step 4: Since the weights sum to 1, the weighted average speed is:

Therefore, the average speed of the roller coaster is 69.25 km/h.