Hi, there--

THE PROBLEM:
A 36 mcm pipe is cut into two pieces in the ratio of 1:2. How long is each pipe?

A SOLUTION:
We know that the pipe is 36mcm. The ratio of 1:2 tells us that after the cut, one piece is two times 
longer that the other. For example, if the short piece is 5mcmc, the long one is 10mcm. If the short
piece is 6mcm, the long piece is 12.

One way to solve this is through trial and error. We keep scaling up until we find a combination whose 
sum is 36mcm. For example,

5 + 10 = 15 too small
6 + 12 = 18 too small
7 + 14 = 21 too small

15 + 30 = 45 too large

12 + 24 = 36 just right!

This is a good method when you aren't sure that's going on. You use trial and error and look for patterns. 
For instance, I notice that when I make the short piece 1 mcmc longer, the length of the whole pipe grows 
by 3 mcmc.

This method can be time consuming, though. Here is a way to use algebra to speed things along.

Let x length of the short piece. Then the long piece must be 2x because the ratio is 1:2.

When we add the lengths of the cut pieces together, the sum is 36mcm. So,
x + 2x = 36

Now solve for x. Combine like terms. (x+2x=3x.)
3x = 36

Divide both sides by 3. (3x/3 is x and 36/3 is 12.)
3x/3 = 36/3
x = 12

In the context of this problem, x=12 means that the sort pipe is 12 mcm long. The longer pipe is
twice as long or 24mcm.


Hope this helps! Feel free to email if you have any questions about the solution.

Good luck with your math,

Mrs. F
math.in.the.vortex@gmail.com