Sarah lives on a block that's 1,600 square feet and 567 inches and she walks 50 steps per every hour picking up 5 pounds of gravel every 7 seconds and grinds it. How many gravel does she collect if she walks her entire block.

To determine how much gravel Sarah collects, we'll need to calculate a few things:

1. The total time Sarah spends walking around the block.
2. The total amount of gravel she collects in that time.

Let's break it down step-by-step.

### Step 1: Area Conversion
The block size is given in square feet and inches. First, we need to ensure uniformity in units for easier calculations. Since area in square feet and inches doesn't make sense together, we'll convert the inches into feet.

567 inches = \( \frac{567}{12} \) feet = 47.25 feet.

So, the block size is 1600 square feet + 47.25 square feet = 1647.25 square feet.

### Step 2: Perimeter Calculation
Assuming the block is a square (which is common in many problems unless specified otherwise):

\[ \text{Side length} = \sqrt{1647.25} \approx 40.59 \text{ feet} \]

The perimeter of the square block is:
\[ 4 \times 40.59 = 162.36 \text{ feet} \]

### Step 3: Steps Calculation
Sarah walks 50 steps every hour. We need to know how many steps she takes per foot to determine the time she spends walking around the block.

However, we need additional information regarding her stride length to find the number of steps per foot. Assuming an average stride length of 2.5 feet per step:

\[ \text{Number of steps per foot} = \frac{1}{2.5} = 0.4 \text{ steps/foot} \]

Thus, walking the perimeter of the block:
\[ 162.36 \text{ feet} \times 0.4 \text{ steps/foot} = 64.944 \text{ steps} \]

### Step 4: Gravel Collection
Sarah picks up 5 pounds of gravel every 7 seconds.

First, calculate the total number of seconds she spends walking.

Sarah takes 64.944 steps at a rate of 50 steps per hour:
\[ \text{Total time walking} = \frac{64.944 \text{ steps}}{50 \text{ steps/hour}} = 1.29888 \text{ hours} \]

Convert hours to seconds:
\[ 1.29888 \text{ hours} \times 3600 \text{ seconds/hour} = 4675.968 \text{ seconds} \]

Now calculate the amount of gravel she collects in this time:
\[ \text{Gravel collected} = \frac{4675.968 \text{ seconds}}{7 \text{ seconds/pickup}} \times 5 \text{ pounds/pickup} \]

\[ = 667.9954 \times 5 = 3339.977 \text{ pounds} \]

### Conclusion
Sarah collects approximately 3340 pounds of gravel while walking around her entire block.

Would you like more details or have any questions?

Here are some related questions:
1. What would be the impact if Sarah's stride length was different?
2. How would the time change if Sarah walked faster or slower?
3. How much gravel would Sarah collect if she walked for a different duration?
4. What if the block was a different shape? How would that affect the calculation?
5. How would changing the frequency of picking up gravel affect the total amount collected?
6. What is the average weight Sarah can carry before needing a break?
7. How would the collected gravel weight change if she picked up more or less gravel each time?
8. How does the block size influence the total walking time and collected gravel?

**Tip:** Always double-check unit conversions to ensure accuracy in multi-step problems.

Explore how Sarah collects gravel while walking around her 1,600 square feet block. Learn step-by-step calculations for area conversion, perimeter calculation, steps calculation, and gravel collection based on her walking speed and pickup rate.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation