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

eddy2017 said:
t= w * r( of speed)
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I realize this is a long thread, but if you don't remember, please go back and find the expression which I confirmed as correct. t= w * r is not correct. If you remember I suggested doing exercises to become more proficient in manipulating expressions. You should not be making mistakes like this twice in the same thread. If r=w/t, then t is not w*r. As I wrote above, you already derived the right formula, doing it again wastes time AND increases the probability of a mistake.
 
eddy2017 said:
t= w * r( of speed)
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I wrote this:
Rate = work/time
r= 240ft^2/3 hrs
r=80 ft^2 per h.
that is the rate of speed.
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And you say:
Good. Now the last step - plug in this rate and the right amount of work into the expression for the second wall time.
That was how we agreed to express the whole thing.
 
eddy2017 said:
I wrote this:

And you say:
Good. Now the last step - plug in this rate and the right amount of work into the expression for the second wall time.
That was how we agreed to express the whole thing.
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This is the expression for the rate. Please go further back to where we derived the expression for the TIME for the second wall. Time = ???
 
lev888 said:
This is the expression for the rate. Please go further back to where we derived the expression for the TIME for the second wall. Time = ???
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you mean this expression you wrote?
If a=b/x, what is x?
 
lev888 said:
I used a=b/x as a hint so you could figure out the expression for time. Again, please find the expression for time. Time = ?
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at post 64 you wrote this:
So, t = w/r. If we plug in correct values we'll be all set. Do we know w or r?
That should be the expression that you are talking about.
 
eddy2017 said:
at post 64 you wrote this:
So, t = w/r. If we plug in correct values we'll be all set. Do we know w or r?
That should be the expression that you are talking about.
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Correct. Can I ask why this step was so difficult? Was it not clear what I meant by "find the expression for time, t = ?"
 
lev888 said:
Correct. Can I ask why this step was so difficult? Was it not clear what I meant by "find the expression for time, t = ?"
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Caught me surprise. But it is a valid one. I just had to go back and review all posts but then I didn't seem to find it, until now that I laid eyes on it. I said, this is it. This is the one. Thanks.
 
eddy2017 said:
Caught me surprise. But it is a valid one. I just had to go back and review all posts but then I didn't seem to find it, until now that I laid eyes on it. I said, this is it. This is the one. Thanks.
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If the solution is clear, can you combine all steps in one post? Feel free to copy/paste from previous posts.
 
lev888 said:
If the solution is clear, can you combine all steps in one post? Feel free to copy/paste from previous posts.
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Here's the solution.
If it takes a student 3 hours to paint a rectangular wall that measures 24 feet by 10 feet, working at the same speed, how long should it take him to paint a wall that measures 16 feet by 18 feet?
1. What do we need to find? Time for the second wall.
2. What's the relationship connecting time, work and rate? Rate2=Work2/Time2. Since we need time, let's rearrange it: Time2=Work2/Rate2
3. We know work: 16*18 sq ft. We don't know rate.
4. Rate is the same as for the first wall.
5. What do we need to find? Rate for the first wall.
6. What's the relationship connecting time, work and rate? Rate1=Work1/Time1
7. We know work: 24*10 sq ft. We know time: 3 hours. Rate = 24*10 sq ft./ 3 hours = 80 sq ft/hour
8. Now we go back and plug in found rate into the time expression in #2: time = 16*18 sq ft./(80 sq ft/hour) = 288/80 hours.

Note the same questions used to guide the thinking process: What do we need to find? What's the relationship connecting a, b, c?

Find a few more work problems and practice this method.
 
lev888 said:
Here's the solution.
If it takes a student 3 hours to paint a rectangular wall that measures 24 feet by 10 feet, working at the same speed, how long should it take him to paint a wall that measures 16 feet by 18 feet?
1. What do we need to find? Time for the second wall.
2. What's the relationship connecting time, work and rate? Rate2=Work2/Time2. Since we need time, let's rearrange it: Time2=Work2/Rate2
3. We know work: 16*18 sq ft. We don't know rate.
4. Rate is the same as for the first wall.
5. What do we need to find? Rate for the first wall.
6. What's the relationship connecting time, work and rate? Rate1=Work1/Time1
7. We know work: 24*10 sq ft. We know time: 3 hours. Rate = 24*10 sq ft./ 3 hours = 80 sq ft/hour
8. Now we go back and plug in found rate into the time expression in #2: time = 16*18 sq ft./(80 sq ft/hour) = 288/80 hours.

Note the same questions used to guide the thinking process: What do we need to find? What's the relationship connecting a, b, c?

Find a few more work problems and practice this method.
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I was going to do it Mr lev. I was just taking a break for the day. But that was good. All your explanations have been great. Yes, I will do some more. The proportion method worked out alright but exploring this formula was excellent.
Thank you,
And thanks to you Mr Jomo.
Have a great evening!.
I'll be back tomorrow.
 
Eddy, you should not be confused in solving a=b/x for x, c=d/x for x, e=f/t for t. Why would this take you by surprise.

OK, so this does take you by surprise. I (and ever other helper here) would advise you to learn how to solve formula like the ones above including r=d/t for t before moving on. I promise you that this is good advice. As you know you need a solid foundation before moving on in math.
 
Jomo said:
Eddy, you should not be confused in solving a=b/x for x, c=d/x for x, e=f/t for t. Why would this take you by surprise.

OK, so this does take you by surprise. I (and ever other helper here) would advise you to learn how to solve formula like the ones above including r=d/t for t before moving on. I promise you that this is good advice. As you know you need a solid foundation before moving on in math.
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Yes, sir. I am always practicing. Word problems are not easy. I think they might be the most challenging thing that Math may have. Thank you so much.
I am studying every day. Would love if you all can recommend a book thst was helpful to you for solving problems.
 
eddy, the concern I am having has nothing to with word problems. Can you not follow that? lev asked you multiple time to solve for t in r=d/t. Thi is not a word problem.
 
Jomo said:
eddy, the concern I am having has nothing to with word problems. Can you not follow that? lev asked you multiple time to solve for t in r=d/t. Thi is not a word problem.
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I know how to do that. I just got confused.
t= r * d
 
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