Installing ceiling panels

Before I give you the solution, I will point out that Buddy and Ken's rate is $\frac{1}{10}$ of a panel per minute and Tom and Leonard's is $\frac{1}{15}$ of a panel per minute. We're trying to find the number of minutes so that's x. So far we have this:

BK's rate = $\frac{1}{10}$ TL's rate = $\frac{1}{15}$ 12 ceiling panels x = time in minutes

So now, we add the amount of work that BK can do to the amount of work that TL can work; and that has to equal 12.

Then we connect the x to the end of the numbers and add the 12 to the other side, and this is what we get: $\frac{1}{10}$ x + $\frac{1}{15}$ x = 12

Next we need to combine the x-terms and put the fraction together, and after reducing it, it comes out to this: $\frac{1}{6}$ x = 12 next, to divide the fraction by x, but it's easier to multiply both sides by the reciprical of $\frac{1}{6}$ , which is $\frac{6}{1}$ which equals 6. On the left side it leaves us with x, and on the right it leaves us with: $x=72$ which is the answer to this problem.