Simple, Speed Rate Multiple Choice Question.

Question

Two people working together can do a job in 3 hrs. How long will it take the slower person to do the same job if one of them is 3 times as fast as the other?

A) 1 hr

B) 1.5 hr

C) 1/3

D) 4 hr

$$WORK$$ Together 1 job in 3 hours = $\frac{1}{3}$

X = Time

Slower Person = $\frac{1}{3x}$

Faster Person = $\frac{1}{x}$

$$Equation$$ $$\frac{1}{x}+\frac{1}{3x}=\frac{1}{3}$$ After solving x=4 (it takes 4 hrs for the fastest person to do 1 job )

To find the slowest person we plug x into $\frac{1}{3x}$

We get 12 hours for the slowest person to do 1 job.

The problem is that 12 hrs is not in the answers, Did I did something wrong?

Answer 1

Your explanation is hard to follow, but the slower person taking $12$ hours and the faster taking $4$ hours is correct. Clearly the intended answer is $4$ hours as that is the only choice longer than $3$ hours and having only one person work must take longer. Probably the slower in the question is a misprint for faster, when $4$ hours would be correct.

Answer 2

To check your answer we can try another approach.
Suppose that the speed of the slower person is x per hr, then the speed of the faster person is 3x per hr.
The amount of job is $3(x+3x)=12x$
The time it takes for the slower person to complete the job is therefore $\frac{12x}{x}=12$ hrs
I think you got the right answer, probably something wrong with the question.