you are preparing a section of steel pipe as shown. the total length of the section will be 9 feet. there…

you are preparing a section of steel pipe as shown. the total length of the section will be 9 feet. there will be an elbow fitting on each end, and 3 tee fittings spaced evenly between them as shown. each elbow is $\frac{3}{4}$ inch and each tee is $1\frac{1}{2}$ inches. how long should each of the 4 pieces of pipe be, in inches?\na $2\frac{1}{4}$\nb 3\nc $25\frac{1}{2}$\nd 27\ne 102

you are preparing a section of steel pipe as shown. the total length of the section will be 9 feet. there will be an elbow fitting on each end, and 3 tee fittings spaced evenly between them as shown. each elbow is $\frac{3}{4}$ inch and each tee is $1\frac{1}{2}$ inches. how long should each of the 4 pieces of pipe be, in inches?\na $2\frac{1}{4}$\nb 3\nc $25\frac{1}{2}$\nd 27\ne 102

Answer

Answer:

C. $25\frac{1}{2}$

Explanation:

Step1: Convert total length to inches

Since 1 foot = 12 inches, 9 feet = $9\times12=108$ inches.

Step2: Calculate total length of fittings

There are 2 elbow fittings and 3 tee - fittings. Each elbow is $\frac{3}{4}$ inch and each tee is $1\frac{1}{2}=\frac{3}{2}$ inches. The total length of elbow fittings is $2\times\frac{3}{4}=\frac{3}{2}$ inches. The total length of tee - fittings is $3\times\frac{3}{2}=\frac{9}{2}$ inches. The total length of all fittings is $\frac{3}{2}+\frac{9}{2}=\frac{3 + 9}{2}=6$ inches.

Step3: Calculate total length of pipes

Let the length of each of the 4 pipes be $x$ inches. The total length of the 4 pipes is $4x$ inches. We know that the total length of the section (pipes + fittings) is 108 inches. So, $4x+6 = 108$. Subtract 6 from both sides: $4x=108 - 6=102$ inches.

Step4: Solve for length of one pipe

Divide both sides by 4: $x=\frac{102}{4}=25\frac{2}{4}=25\frac{1}{2}$ inches.