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Comment on Curt & Omar Paint a Fence
Hello: I did this:
Omar's time= 1/D
Curt's time= 1/2D
S=1/8
I set them equal to 1/4, cleared fractions, and I got 8+4+D=2D. Solving I got D (which is the variable I used for Omar again) and got D=12. Why wouldn't Curt's time be 6 then? What did I do wrong?
First of all, I'm assuming
First of all, I'm assuming that, when you say Omar's time = 1/D, you actually mean Omar's RATE = 1/D, where D = the number of hours (time) it takes Omar to pain the fence.
Since Curt can paint the fence in HALF the time it takes Omar to paint the fence, then we know that Curt's rate is TWICE Omar's rate.
So, if Omar's rate = 1/D, then Curt's rate is 2/D (not 1/2D as you have in your solution).
So, we get: 1/D + 2/D + 1/8 = 1/4
Multiply both sides by 8D to get: 8 + 16 + D = 2D
Solve to get: D = 24
This means Curt's rate = 2/D = 2/24 = 1/12 (1/12 of the fence in 1 hour)
So, Curt will take 12 hours to paint the ENTIRE fence.
Hi Brent! Another question:
Close!!
Close!!
Presumably, your variables represent how much of the job is completed in ONE HOUR
Let x = number of hours it takes Omar to paint the fence.
So, 1/x = fraction of the job Omar completes in ONE HOUR
Then 2/x = fraction of the job Curt completes in ONE HOUR (you have x/2). We can conclude this because we're told that Curt is twice as fast as Omar.
Also, 1/8 = fraction of the job Saul completes in ONE HOUR
So, in ONE HOUR the three mean can complete 1/x + 2/x + 1/8 of the job. We're told that, working together, the men can complete 1/4 of the job in ONE HOUR
So, we can write: 1/x + 2/x + 1/8 = 1/4
Solve to get x = 24. So, it takes OMAR 24 hours to paint this fence, which means Curt can paint it in 12 hours.
Thank you for clearing up the
Curt +Omar +fence=4
Tyner why u have mentioned 1/4?
I'm not sure what you mean by
I'm not sure what you mean by "Curt +Omar + fence = 4"
In my solution, the 1/4 represents the HOURLY RATE of the men working together. That is, since they can complete the entire job in 4 hours, then in ONE HOUR, they can complete 1/4 of the job.
Is there another way to solve
Rate of Saul = 1/8
Combined rate of 3 men = 1/4
Now 1/4-1/8 will give me combined rate of Curt and Omar.
It is 1/8. Now curt and Omar can paint together in 8 hours. Now how to split 8 such that one part is half of another? This is my doubt. Please help.
Good start!! I'll continue
Good start!! I'll continue from where you left off.
Once we know that the COMBINED rate of Curt and Omar is 1/8, we can write:
(Curt's rate) + (Omar's rate) = 1/8
Next, we can use the information from the first sentence.
This tells us that Curt's rate is TWICE Omar's rate.
Or we might say that Omar's rate is HALF that of Curt.
So, if we let C = Curt's rate, then C/2 = Omar's rate. This allows us to write:
C + C/2 = 1/8
Multiply both sides by 8 to get: 8C + 4C = 1
Simplify: 12C = 1
So, C = 1/12
If Curt's rate is 1/12 of the house PER HOUR, then it will take Curt 12 hours to paint the ENTIRE house.
Does that help?
Cheers,
Brent