Calculating Weighted Average: Analyzing Roller Coaster Speeds

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.