Activity 1.1.2 Gears - VEX: Understanding gear ratios and compound gear trains in robotics.

I'll solve the problem in the image by following a structured approach.

First, look closely:
The image shows an educational worksheet titled "Activity 1.1.3 Gears - VEX" from PLTW Engineering. It's about compound gear trains and calculating gear ratios.

The specific task I need to solve is:
- Calculate the gear ratio for a compound gear train (Gear Ratio of A:D)
- The formula given is: GR = D₁/D₂ × D₃/D₄
- Where D₁, D₂, D₃, D₄ represent the number of teeth on different gears

From the diagram, I can see:
- Gear A (D₁) has 60 teeth (large green gear)
- Gear B (D₂) has 12 teeth (small green gear)
- Gear C (D₃) has 60 teeth (large yellow gear)
- Gear D (D₄) has 12 teeth (small yellow gear)

The problem asks me to calculate the gear ratio A:D using the formula provided.

Next, find information:
I don't need additional research for this calculation since all the necessary information is visible in the image.

Then, review the findings:
I have all the values needed to plug into the formula:
GR = D₁/D₂ × D₃/D₄
GR = 60/12 × 60/12

Let me calculate this:
GR = 5 × 5 = 25

This means that for every 1 rotation of gear A, gear D will rotate 25 times.

The solution is straightforward since I can directly read the number of teeth from the image and apply the given formula.

Final Answer:
The gear ratio of A:D is 25:1.

This is calculated using the formula GR = D₁/D₂ × D₃/D₄, where:
- D₁ (gear A) = 60 teeth
- D₂ (gear B) = 12 teeth
- D₃ (gear C) = 60 teeth
- D₄ (gear D) = 12 teeth

So, GR = 60/12 × 60/12 = 5 × 5 = 25.

This means gear D rotates 25 times for every single rotation of gear A, which is typical for compound gear trains where multiple gear reductions are combined to achieve a high overall gear ratio.