A drain must be installed with a grade of 

one sixth16 

in. of vertical drop per foot of horizontal run. How much of a drop will there be for 

3838 

ft of​ run?

Question content area bottom

Part 1

For 

3838 

ft of​ run, there will be 

enter your response here 

in. of drop.

​(Type a whole​ number, proper​ fraction, or a mixed​ number.)

To solve this problem, you need to calculate the total vertical drop for a horizontal run of 38 feet, given a grade of \(\frac{1}{16}\) inch per foot.

### Step 1: Understand the relationship
- The problem states that the drain should drop \(\frac{1}{16}\) inch for every 1 foot of horizontal run.

### Step 2: Calculate the total drop
- For a 38-foot run, the total drop will be:
  \[
  \text{Total drop} = 38 \times \frac{1}{16} \text{ inches}
  \]
  \[
  \text{Total drop} = \frac{38}{16} \text{ inches}
  \]

### Step 3: Simplify the fraction
- Simplify \(\frac{38}{16}\) by dividing both the numerator and the denominator by their greatest common divisor (which is 2):
  \[
  \frac{38 \div 2}{16 \div 2} = \frac{19}{8} \text{ inches}
  \]

### Step 4: Convert to a mixed number
- \(\frac{19}{8}\) can be written as a mixed number by dividing 19 by 8:
  \[
  19 \div 8 = 2 \text{ remainder } 3
  \]
  So, \(\frac{19}{8} = 2 \frac{3}{8}\).

### Final Answer
For a 38-foot run, there will be **\(2 \frac{3}{8}\) inches** of drop.

Would you like further details or have any questions?

Here are 5 related questions:

1. How would you calculate the drop for a run of 50 feet at the same grade?
2. How do you convert a fraction like \(\frac{19}{8}\) to a decimal?
3. What is the process to find the greatest common divisor of two numbers?
4. How would the drop change if the grade was \(\frac{1}{12}\) inch per foot?
5. How do you interpret and apply the concept of slope in practical situations?

**Tip:** When working with fractions, always check if they can be simplified to make calculations easier and results clearer.

Learn how to calculate the vertical drop for a drain installation with a horizontal run of 3838 feet, given a grade of one sixth16 inch per foot. Follow a detailed step-by-step solution to determine the total drop in inches. Suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation