A plumber has a very long piece of pipe that is used to run city water parallel to a major roadway. The pipe is cut into two sections. One section is 12 ft. shorter than the other. If 34 of the length of the shorter pipe is 120 ft., how long is the longer piece of pipe? Solve algebraically,
Let x = the shorter piece. Let y = the longer piece.
(3/4)x = 120
x = 120 / (3/4)
x = 120 * (4/3 = 480/3 = 160 feet
y = 160 + 12
172 feet
Let's denote the length of the longer piece of pipe as x ft.
According to the information given, the length of the shorter piece is 12 ft less than the longer piece, so its length can be represented as (x - 12) ft.
We are told that 34 of the length of the shorter pipe is 120 ft. This means that 34% of the length of the shorter pipe is equal to 120 ft.
To find the length of the shorter pipe, we can set up the following equation:
0.34 * (x - 12) = 120
Simplifying the equation, we have:
0.34x - 4.08 = 120
Now, let's isolate the variable x by moving the constant term to the other side:
0.34x = 120 + 4.08
0.34x = 124.08
Finally, divide both sides of the equation by 0.34 to solve for x:
x = 124.08 / 0.34
x ≈ 364.7
Therefore, the longer piece of pipe is approximately 364.7 ft long.
To solve this problem algebraically, let's denote the length of the shorter piece of pipe as x.
We are given that 34 of the length of the shorter pipe is 120 ft. In other words, (34/100) * x = 120.
To find the length of the longer piece of pipe, we need to find the length of the shorter piece first. Rearranging the equation, we have:
(34/100) * x = 120
Multiply both sides by 100 to remove the fraction:
34x = 12000
Next, we need to find the value of x. Divide both sides by 34:
x = 12000 / 34
x ≈ 352.94 ft (rounded to two decimal places)
Since we are given that the shorter pipe is 12 ft. shorter than the longer pipe, we can find the length of the longer pipe by adding 12 ft. to the length of the shorter pipe:
Length of longer pipe = x + 12
Length of longer pipe ≈ 352.94 + 12
Length of longer pipe ≈ 364.94 ft (rounded to two decimal places)
Therefore, the longer piece of the pipe is approximately 364.94 ft long.