Question

Samantha and Kylee are bakers. If Samantha can decorate a cake in 5 hours and Kylee 8 hours to decorate a cake, how long will it take if they worked together. Explain each step in solving this equation.

Answer 1

3 1/13 hours

Explanation:

Lets create a variable:

Samantha and Kylee together (NOT the answers) =
`T_(SK)`

Now lets create an equation:

`1/T_(SK) = 1/T_(S) +1/T_(K)`

Let's look at the time Samantha and Kylee takes to decorate the cake by themselves:

Samantha: 5 hours

Kylee: 8 hours

Let's create an equation to find the answer now:

`1/T_(SK) = 1/5 + 1/8`

Note that now that's its basically algebra, change the variable to
`x` like this:

`1/x = 1/5 +1/8`

Now let's find the LCM (Lowest Common Multiple) of 5, 8, and
`x` which is 40
`x`.

`40 = 8x + 5x`

`40 = 13x`

`13x = 40`

`x = 40/13`

`x` = 3 1/13 hours

Please note that the step where it swapped 13
`x` and 40 is only my way, it is not necessary, it's just my own comfort.