how long should it take him to paint a wall that measures 16 feet by 18 feet?

Let's do everything systematically.
First of all, please look at your answers critically: does "rate of speed is 3 hours" make sense? No. rate is measured in units of something per unit of time. This is not a competition, you don't get bonus points for fast answers - take your time to review them. Critically.

So, you are right, the rate for the second wall is not immediately known.
What do we do next? Exactly the same thing as in the first step, when we addressed the 'main' unknown'.
We identified the question - what is the rate for the second wall.
Then we write down the relationship that connects the rate to other quantities in the problem (work and time):
rate = work/time

We don't need to rearrange it since rate is already on the left hand side.
Do we have work and time specified in the problem that we can plug into this expression to calculate the rate?
 
Look Again suggested using the proportion \(\displaystyle \frac{x hours for Wall2}{number of hours for Wall1}= \frac{number of square feet of Wall2}{number of square feet of Wall1}\).

Since the problem specifically says that the walls were painted at the same speed,
I would have suggested set the rate at which the walls are painted equal.

That would be \(\displaystyle \frac{number of square feet of Wall2}{x hours for Wall2}= \frac{number of square feet of Wall1}{number of hours for Wall1}\).


Since \(\displaystyle \frac{a}{b}= \frac{c}{d}\) is equivalent to \(\displaystyle \frac{c}{a}= \frac{d}{b}\) those are really the same.
 
eddy2017 said:
Let's do everything systematically.
First of all, please look at your answers critically: does "rate of speed is 3 hours" make sense? No. rate is measured in units of something per unit of time. This is not a competition, you don't get bonus points for fast answers - take your time to review them. Critically.

So, you are right, the rate for the second wall is not immediately known.
What do we do next? Exactly the same thing as in the first step, when we addressed the 'main' unknown'.
We identified the question - what is the rate for the second wall.
Then we write down the relationship that connects the rate to other quantities in the problem (work and time):
rate = work/time

We don't need to rearrange it since rate is already on the left hand side.
Do we have work and time specified in the problem that we can plug into this expression to calculate the rate?
Click to expand...
we have the work = 16 * 18 ft^2 which amounts to 288 ft^2.
time is the unknow. I don't have it.
rate of speed: I only read this info in the problem. Working at the same speed.
3 hours is not the speed. because like you said, rate of speed is like in 'miles per gallon', there has to be a ratio involved, a per..., and is not there.
That is all I see so far.
thank your interest, Mr lev. Thank you.
 
HallsofIvy said:
Look Again suggested using the proportion \(\displaystyle \frac{x hours for Wall2}{number of hours for Wall1}= \frac{number of square feet of Wall2}{number of square feet of Wall1}\).

Since the problem specifically says that the walls were painted at the same speed,
I would have suggested set the rate at which the walls are painted equal.

That would be \(\displaystyle \frac{number of square feet of Wall2}{x hours for Wall2}= \frac{number of square feet of Wall1}{number of hours for Wall1}\).


Since \(\displaystyle \frac{a}{b}= \frac{c}{d}\) is equivalent to \(\displaystyle \frac{c}{a}= \frac{d}{b}\) those are really the same.
Click to expand...
That is a nice tip, Mr H. Thanks. I will finish with Mr lev and give this a good look too.
Even though I think the proportion that I set was properly set, this one looks very neat.
 
eddy2017 said:
we have the work = 16 * 18 ft^2 which amounts to 288 ft^2.
time is the unknow. I don't have it.
rate of speed: I only read this info in the problem. Working at the same speed.
3 hours is not the speed. because like you said, rate of speed is like in 'miles per gallon', there has to be a ratio involved, a per..., and is not there.
That is all I see so far.
thank your interest, Mr lev. Thank you.
Click to expand...
I answer your questions to the best of my ability. let's keep this flowing to finish. Let's keep at it. Correct me or give hints again, pls. Thanks.
 
eddy2017 said:
we have the work = 16 * 18 ft^2 which amounts to 288 ft^2.
time is the unknow. I don't have it.
rate of speed: I only read this info in the problem. Working at the same speed.
3 hours is not the speed. because like you said, rate of speed is like in 'miles per gallon', there has to be a ratio involved, a per..., and is not there.
That is all I see so far.
thank your interest, Mr lev. Thank you.
Click to expand...
Ok, you noticed "Working at the same speed" - this is important. This allows us to use the rate for first wall in the expression for the second wall time above.
Now, can we calculate the rate for the first wall? You know the formula. Do we have enough information?
 
lev888 said:
Ok, you noticed "Working at the same speed" - this is important. This allows us to use the rate for first wall in the expression for the second wall time above.
Now, can we calculate the rate for the first wall? You know the formula. Do we have enough information?
Click to expand...
Rate = work/time
r= 240ft^2/3 hrs
r=80 ft^2 per h.
that is the rate of speed.
 
lev888 said:
Good. Now the last step - plug in this rate and the right amount of work into the expression for the second wall time.
Click to expand...
second wall
r = w/t
80 ft^2 per h= 18 * 16 ft^2/t
80 ft^2 per h= 288 ft^2/t
I will divide 80 into both sides
t=3.6 time needed to paint the second wall.
 
eddy2017 said:
second wall
r = w/t
80 ft^2 per h= 18 * 16 ft^2/t
80 ft^2 per h= 288 ft^2/t
I will divide 80 into both sides
t=3.6 time needed to paint the second wall.
Click to expand...
No, you should have the expression for time. T= ?
I am trying to show how to solve such problem in an efficient way. If you already have an expression for time you don't need to derive it again.
 
lev888 said:
No, you should have the expression for time. T= ?
I am trying to show how to solve such problem in an efficient way. If you already have an expression for time you don't need to derive it again.
Click to expand...
Sorry,
t=3.6 hours needed to paint the second wall.
 
eddy2017 said:
Sorry,
t=3.6 hours needed to paint the second wall.
Click to expand...
Thanks for staying and guiding me till the solution. It is the only way to learn for real.
If we were to check if 3.6 h is a valid answer, how would we go about it?.
 
eddy2017 said:
I don't get it, sir.
Click to expand...
I wrote: "Now the last step - plug in this rate and the right amount of work into the expression for the second wall time. "
If you did it, then you must know which expression you used. I am asking you to post it. Not just the answer.
 
lev888 said:
I wrote: "Now the last step - plug in this rate and the right amount of work into the expression for the second wall time. "
If you did it, then you must know which expression you used. I am asking you to post it. Not just the answer.
Click to expand...
Oh,
Rate = work/time
 
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