Jim can fill a pool carrying bucks of water in 30 minutes.

[natalieh]

Please help me figure out this story problem, a sample of many I have to take on a Nursing entrance exam tomorrow...thanks!

If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks?

or

Jim can fill a pool carrying bucks of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ½ hours. How quickly can all three fill the pool together?

I can't figure out how to set this up! Thank you!

 

[galactus]

Re: Help. I have a math test to take on Sunday...

Jim can fill a pool carrying bucks of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ½ hours. How quickly can all three fill the pool together?

Think about how much of the pool can be filled by each in one minute.

\(\displaystyle \L\\\frac{1}{45}+\frac{1}{30}+\frac{1}{90}=\frac{1}{t}\)

Solve for t.

 

[tkhunny]

Re: Help. I have a math test to take on Sunday...

If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks?

There's something socially wrong with this question, nevertheless...

Steve: 20/5 dpm = 4 dpm
Sue: 20/10 dpm = 2 dmp
Jack: 20/15 dpm = (4/3) dpm

Add them up: (4 + 2 + 4/3) dpm = (6 + 4/3) dpm = (22/3) dpm

Working at (22/3) dpm, how long does it take to make 20?

 

[natalieh]

Thank you! Never would have come up with the set-up, especially with the pool filling....

 

[Mrspi]

Re: Help. I have a math test to take on Sunday...

If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks?

The "job" here is making 20 drinks.

Steven can do the job in 5 minutes, so each minute he does 1/5 of the job.
Sue can do the job in 10 minutes, so each minute she does 1/10 of the job.
Jack can do the job in 15 minutes, so each minute he does 1/15 of the job.

Now...let t = time it takes the three of them together to do the job.

Steve does t/5 of the job. Sue does t/10 of the job. Jack does t/15 of the job.

Steve's part + Sue's part + Jack's part = whole job

t/5 + t/10 + t/15 = 1

Multiply both sides of the equation by the least common denominator of all the fractions, which is 30:

30(t/5) + 30(t/10) + 30(t/15) = 30*1

6t + 3t + 2t = 30

Now....can you finish it?

 

[natalieh]

I think I've got it. Several people emailed me the same set up - hopefully I won't panic under pressure tomorrow as the math test is a timed test.

thank you so much....natalie

 

[tkhunny]

People emailed you from this site? Or perhaps others from whom you asked? The point would be that a public response can benefit many. Who would choose to email rather than post on the public boards?