How can i do this math problem?

Question

If they worked together, Rose and Jeff can winterize and close the swimming pool in 5 hours. If it takes Rose 9 hours to close the pool herself, how long would it take Jeff to do it by himself?

Answer 1

9*b/(9+b)=5

9b=5*(9+b)

9b=45+5b

4b=45

b=45/4=10 hours 15 minutes.

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Answer 2

Let R be roses rate of work.

Let J be Jeff's rate of work.

Let w = work.

time is work/rate.

so we know that Rose takes 9 hours So her rate of work is 1 because 9h=9w/1r.  If we had two of Rose then the time would be Hours=9w/(R+R).  Since the rate of R=1 the time is 4.5 hours. So we know that Jeff is slower.

  

In other words, in five hours, they did the 9 hours worth of work together.

time = work/rate.

rate= work/time

rate of both = 9/5

both are 1.8.  We already know that Rose is one so Jeff is 0.8

The question now is how long will it take for Jeff by himself?

time = 9/.8

so jeff woud take 11 hours 15 minutes.

Answer 3

I would say the same 9 hours as rose or about 3 hours is my second answer

Answer 4

less than 4 hours than Rose. ( - 4)

Answer 5

The real-world answer is, there's no telling.  But that's not going to help you with your math homework.

In math class, we assume that Rose and Jeff will both work at constant rates, and that those rates don't change whether they're working together or separately.

The trick here is to rephrase the problem in terms of speed-of-working.  Rose and Jeff combined can do 1/5 of the job per hour.  Rose by herself can do 1/9 of the job per hour.  The difference is Jeff's speed-of-working.

1/5 - 1/9

9/45 - 5/45

4/45

Ok, 4/45 of the job per hour is rather awkward.  But, we can now turn Jeff's speed-of-working back into a duration for the job.

45/4 hours

11 1/4 hours

11 hours, 15 minutes.

Answer 6

9 hours. I dont see why it should be different.