Question

Hoang has worked as a nurse at Springfield General Hospital for 5 years longer than her friend Bill. Five years ago, she had been at the hospital for twice as long. How long has each been at the hospital?

Answer 1

• Hoang: 15 years
• Bill: 10 years

Explanation:

You want to know how long Hoang and Bill have worked at the hospital if Hoang has worked there 5 years longer, and 5 years ago that was twice as long as her friend Bill.

Thinking about it

Hoang's longevity will be twice Bills when Bill's is equal to the difference. That is, 5 years ago, Bill had been there 5 years and Hoang had been there 10 years.

Now, each has been there 5 years longer, so ...

• Hoang has been there 15 years
• Bill has been there 10 years

Equation

If h represents Hoang's time at the hospital, 5 years ago it was (h-5). Currently, Bill's time at the hospital is (h-5), and 5 years ago it was (h-10). The relation between the times 5 years ago is ...

(h -5) = 2(h -10)

15 = h . . . . . . . . . . add 20-h to both sides

h-5 = 15 -5 = 10 . . . . Bill's time at the hospital

Hoang and Bill have been at the hospital 15 years and 10 years, respectively.