Simple algebra II

[intothevoidx]

I was wondering if someone could help me with this word problem. I am terrible with word problems.....I need you to explain it in steps and tell me why you are doing what you are doing. I greatly appreciate it.

 

 

Tom and Huck start a business painting fences. They paint Aunt polly's fence and find that they can paint a 200 square foot fence in 40 minutes if they work together/ If huck works 4 times faster than tom, how long would it take each of them to paint a 500 square ft fence working alone?

[timo]

I was wondering if someone could help me with this word problem. I am terrible with word problems.....

Surprisingly, many people are. Sadly, some people think that solving equations is more important than the initial step of transfering a problem to equations. This is not true. You will seldomly be welcomed by two equations on a train station while the question whether a group ticket might be a better bargain than individual tickets -even if two of your group only go for half the distance- might indeed arise.

I´m not imposting that you are one of those "text exercises suck"-people but if you´re bad at them, you should really try to improve your skill here. The trick actually is to translate the information given into mathematical expressions (here it´s equations). Sadly, I wouldn´t know of any cooking recipe how to do it - I do it rather intuitively (experience plays a big role, though).

 

I need you to explain it in steps and tell me why you are doing what you are doing.

I don´t think giving a step-by-step guide is much of a help for you, here. So I´ll tell you what I see when I look at above problem, instead:

- There is two parameters/variables/answers that´s asked for, namely the working speed of Tom and the working speed of Huck.

- There is two informations given, namely their combined working speed ("They paint Aunt polly's fence and find that they can paint a 200 square foot fence in 40 minutes if they work together") and the ratio of their working speeds ("huck works 4 times faster than tom"). If this is not obvious to you, take some time and think about it. Extracting informations from a text is one of the keys to solve text exercises.

- These two informations can each be cast into a mathematical form - an equation in this case.

- Now you have a "two equations/two unknowns" problem in mathematical form. Solving it is only technicality, now - and since you are given that exercise I assume you learned how to do that recently.

[hotcommodity]

I got 500 min. for one and 170 for the other. but I could be wrong.

[intothevoidx]

I have trouble putting the information into equations.....I know one of them is x and the other 4x but after that I have no idea what to do.

[intothevoidx]

I got 500 min. for one and 170 for the other. but I could be wrong.

 

 

The answer is 500 and 125....I just need to know how to perform this kind of word problem. I am going to have an anyeurism soon if I don't figure out how to do this.....

[timo]

- I must confess I was a bit hasty when I said "There is two parameters/variables/answers that´s asked for, namely the working speed of Tom and the working speed of Huck". Actually, it´s the time it takes them to paint the 500 square feet fence which is asked for. However, getting from the working speed to the time the work takes is pretty easy. And solving for their working speeds first seems easier to me.

 

- For converting to equations: I am not sure it helps but maybe it´s worth a try: Try answering these questions:

1) If I paint 10 square feet per minute, how much fence will be painted after 4 minutes?

2) If you help me and paint 15 square feet per minute for the same 4 minutes, how much of the fence will be painted, then?

3) What if I don´t paint 10 square feet per minute but Q square feet per minute - how much square feet of fence will be painted after 4 minutes, then?

4) What if I paint Q square feet per minute and you paint Z times as fast as me?

[intothevoidx]

I don't want you to think I'm being lazy and that I want you to do the problem I am just having problems with the processes that will get you 500 and 125 as your answer. I have all the work that my teacher showed me on my paper but I don't understand why he did what he did. For example I reduce 200/4x and get 50/x then I do the same for tom and get 200/x. Why the heck did I just do that?

[Klaynos]

you've got to think in terms of splitting it down:

 

If huck is 4 times faster than tom, then 4/5ths of the work done was done by him, so he'll be 4/5ths of the rate of painting.

 

From this you can work out the rate both of them work at and from that work out the final bit...

[timo]

@intothevoidx:

I don´t know why you do that. After all, all I know about "x" is that it´s a letter appearing at the end of the alphabet.

No, seriously: All I can offer you is leading you on the way that I would take to solve the problem. I think the steps 1) - 4) in above are really simple questions; step 4 is almost the answer to the original question. There´s not nessecarily always only a single way to solve a problem and how should I or anyone else on this board know how your teacher solved it? If you don´t want to try another way of solving the problem, then post what your teacher wrote down - you´ll surely find someone who can explain it to you.

[intothevoidx]

you've got to think in terms of splitting it down:

 

If huck is 4 times faster than tom' date=' then 4/5ths of the work done was done by him, so he'll be 4/5ths of the rate of painting.

 

From this you can work out the rate both of them work at and from that work out the final bit...[/quote']

 

 

Ok so going by that Huck painted 160 ft in 40 minutes.....Correct? So I divide 160 into 500 and get 3.25 which I multiply by 40 to get the time of 125 minutes and since his time is 1/4 of Huck's I multiply it by 4 to get 500. Ok thanks I understand it now! I wasn't even looking at it in terms of fractions.....Thanks alot for the help I really appreciate it. Nothing feels better than finally understanding a math problem....

[hotcommodity]

I was wondering if someone could help me with this word problem. I am terrible with word problems.....I need you to explain it in steps and tell me why you are doing what you are doing. I greatly appreciate it.

 

 

Tom and Huck start a business painting fences. They paint Aunt polly's fence and find that they can paint a 200 square foot fence in 40 minutes if they work together/ If huck works 4 times faster than tom' date=' how long would it take each of them to paint a 500 square ft fence working alone?[/quote']

 

OK,you got me to sit down and figure it out here it is:

 

if x=work then you have one worker that does x and one that does 4x (4 times the amount of work).

 

together they do 200 sq. ft. so, 4x + x = 200

 

therefore 5x = 200 and x = 40, in other words one guy does 40 sq.ft. every 40 min and the other does 4(40)=160sq. ft. every 40 min.

 

so then you divide 500 by 40 and 160, you get 12.5 and 3 and an eighth respectively.

 

multiply 12.5 and 3 and an eighth by the 40 min and you get your 500 min and 125 min. i hope that helps.