Question

Dominique can ice cupcakes twice as fast as Houston. When they work together, Dominique and Houston can ice a large order of cupcakes in 5 hours. How many hours would it take Houston to ice them by himself?

Answer 1

So what we know from what was given:
\[Houston = 1/x\]
\[Dominique = (1/2x)\]
\[altogether = 1/5\]

Now we have to add
\[1/x + 1/2x = 1/5\]

Let's see if you can do the math from there.

Answer 2

hmm...
I would write it like this
\[Houston = x\]
\[Dominique = 2x\] because he works twice as fast as Houston, so he can get twice the amount of work done as Houston can in a given time period and \[x+2x = 5\]
Once you find x, you will know the number of hours it will take, now if Houston has to do the whole thing himself, it would take him the value for (x) times how many hours? = 5
So basically,
\[x(y)=5\]
Where y is how many hours it will take Houston to do them all himself, and we already solved for x in the previous step so we can plug in that value for x, Ultimately y is your answer.