Question

Hoang has worked as a nurse at Springfield General Hospital for 6 years longer than her friend Bill. Two years ago, she had been at the hospital for twice as long. How long has each been at the hospital?

Answer 1

Ok let's take the information given and make an equations system with it.

I'm gonna use H for Hoang present working years and B for those of Bill. We know that right now Hoang has worked for 6 years longer than Bill, with this we can create the following equation:

`H=B+6`

We also have information from two years ago, at that time Hoang's working years doubled Bill's working years. One would feel tempted to write the equation H=2*B but you have to remember that this information is from the past and H and B stand for working years in the present. The correct way to approach this is change H and B by H-2 and B-2 so we consider that this information is from 2 years ago:

`\begin{gathered} (H-2)=2\cdot(B-2) \\ H-2=2B-4 \\ H-2B=-2 \end{gathered}`

So now we have constructed our equations system:

`\begin{gathered} H=B+6 \\ H-2B=-2 \end{gathered}`

Let's take the outcome of the first equation and use it in the second one:

`\begin{gathered} H-2B=(B+6)-2B=-2 \\ B-2B+6=-2 \\ -B=-2-6=-8 \\ B=8 \end{gathered}`

And going back to the first equation:

`H=8+6=14`

So Hoang has been working at the hospital for 14 years and Bill for 8 years.