Another math problem I don't understand. Can you help me?

Question

A water main for a street is being laid using a particular kind of pipe that comes in either 18-foot sections or 20-foot sections. The designer has determined that the water main would require 14 fewer sections of 20-foot pipe than if 18-foot sections were used. Find the total length of the water main.

Thanks in advance. Please show work

Answer 1

this is pretty simple.

lets say the number of needed mains is x

so the formula should come out: 18x=20(x-14)

which becomes 18x=20x-280. now you just work it out and it's

x=140

140x18=2520

Answer 2

Total length = 20 L (number of long sections)
Total length = 18 S (number of short sectioins)
L-14 = S
20 L =18 S
Substitute
20 L = 18(L-14)
2L = 252
L = 136
Total length is 20 x 136 = 2520 feet

Answer 3

let x= the length of pipe to be laid. it will require x/18 sections of 18' pipe or x/20 sections of 20' pipe. it will take 14 more sections of 18' pipe so

x/18-x/20=14 multiply both sides by 180
10x-9x=14*180=2520
x=2520' of pipe are needed. that can be 2520/18=140 pieces of 18' pipe or 126 pieces of 20' pipe. 140-126=14

the water main will be 2520'

Answer 4

Let L be the length of the water main. The number of 20' lengths needed is L/20; the number of 18' lengths needed is L/18; you need 14 less 20' lengths so

L/20 = L/18 -14

L(1/20 - 1/18)=-14

L = 14/(1/18-1/20)

Answer 5

let x be the total length of the water main and z the amount of 20ft pipes.

x = 20z

18z+ 14 = 20z
14 = 2z
z = 7

x = 20*7
x = 140-foot long water main

Answer 6

18 18 =1584 feet

Answer 7

x=number of 20ft pipes

20x=18(x+14)
20x=18x+252
2x=252
x=126

length of main = 126 pipes * 20ft = 2520ft