Orville visits a circular pond near his home. Over the pond, there is a bridge stretching from one end to the other. The bridge passes directly over the center of the pond. Orville... Orville visits a circular pond near his home. Over the pond, there is a bridge stretching from one end to the other. The bridge passes directly over the center of the pond. Orville likes to walk all the way around the pond and over the bridge to relieve stress. If one of Orville’s steps covers 3 feet and it takes 15 steps to cross the bridge, approximately how many feet would Orville travel if he walked all the way around the pond and over the bridge once? Read more

Steps to Solve

1. Calculate the Length of the Bridge

Orville's steps cover 3 feet, and it takes him 15 steps to cross the bridge.

The length of the bridge can be calculated using the formula: $$ \text{Length of the Bridge} = \text{Number of Steps} \times \text{Feet per Step} $$

So, $$ \text{Length of the Bridge} = 15 , \text{steps} \times 3 , \text{feet/step} = 45 , \text{feet} $$

2. Determine the Diameter of the Pond

Since the bridge passes directly over the center of the pond, and we assume it is a diameter, we have to define its length. For now, let’s denote the diameter of the pond as ( d ) feet.

3. Calculate the Circumference of the Pond

The circumference ( C ) of a circle can be calculated using the formula: $$ C = \pi d $$

For now, we’ll leave it as: $$ C = \pi d $$

4. Total Distance Calculation

To find the total distance Orville walks, we add the circumference of the pond and the length of the bridge: $$ \text{Total Distance} = C + \text{Length of the Bridge} $$ $$ \text{Total Distance} = \pi d + 45 $$

5. Final Answer Formulation

Since the problem does not provide the diameter ( d ), we'll leave the answer in terms of ( d ): $$ \text{Total Distance} = \pi d + 45 $$