Algebra word problems (1 Viewer)

[Kittikhun]

Hello.

Firstly, I don't know where to post this question so I posted it here. I'm sorry if this causes any trouble to anyone.

OK, so how does a person work out these problems algebraically? I've tried but I've failed and my sister isn't back from her holidays yet so I can't ask her. I also wasn't allowed to borrow my year 10 maths textbook over the holidays so I have no idea how to do them. Anyway, I'm probably boring you with irrelevant information so I'll just start. For example-

It takes Trevon ten hours to clean an attic. Cody can clean the same attic in seven hours. Find how long it would take them if they worked together.

I've worked it out but the method I used, and only know of to solve this, was to draw a graph and then point these values on the corresponding y axis and then find the point that they meet and cross and voila, that's the answer. Does anyone know how to solve this algebraically? I feel stupid for not knowing.

Thanks.

 

[cutemouse]

Uhh simultaneous equations with a common variable (eg. 't') of some sort? Lol, I did this stuff in like Year 7 so I can't remember :|

 

[jet]

Well, for something like this, you would say, let the total size of the attic to be cleaned = x m² or something conceptual like that.

Then you say, trevor cleans the attic at A/10 m²/h, whilst Cody can clean it at A/7 m²/h

Basically you would add these rates together as they are cleaning at the same time. So, they can work together at a rate of 17A/70 m²/h
Hence, rearranging the rate you can see that it takes them 70/17 hours = 4.117 hours.

 

[Kittikhun]

So simple and yet I couldn't figure it out.

Thanks a million and to the antecedent poster, you guys learned algebraic word problems in year seven?

 

[cutemouse]

Yes, either Year 7 or Year 8. It's a long time ago. lol, it's not necessary for Year 10+ so I've forgotten.

 

[oasfree]

Well, for something like this, you would say, let the total size of the attic to be cleaned = x m² or something conceptual like that.

Then you say, trevor cleans the attic at A/10 m²/h, whilst Cody can clean it at A/7 m²/h

Basically you would add these rates together as they are cleaning at the same time. So, they can work together at a rate of 17A/70 m²/h
Hence, rearranging the rate you can see that it takes them 70/17 hours = 4.117 hours.

This is a more complex way of thinking. Even after you have done it, you wonder if your method is absolutely correct. I find it quite hazy to think that if you take two speeds, plus together to form the combined speed, then divide the Area by this combined speed to get the reduced combined time. The answer is correct. But the danger is that if kids get taught this way they have to remember this as a "formula" to solve any problem that is similar to this. If they forget, that's too bad at exam time.

Another method to solve it is more of derivation from ratio that is more suitable for little kids to learn. Year 4-6 would have manage this method easier. It's better to use a simpler method to solve the problem.

Here is a simpler solution

Imagine that the JOB is shared between the two kids. One is slow and one is faster. They start from two opposite ends. You would expect that the faster one will be able to do more. And when they meet somewhere, the job is done. Looking at the time of 10 minutes for person A and 7 minutes for person B. You know that person A is slower than person B.

Therefore "speed of A" / "speed of B" is 7/10. This is the ratio we need. That means if we divide the job into 17 parts, person A will take 7 parts and person B will take 10 parts. They will complete their allocated parts in the amount of time if they start working at the same time. That's when they complete the whole job together.

So we have this relationship just based on person A

"The whole job" needs 10 minutes
(7/17) of "the whole job" needs ? minutes

((7/17) / 1 ) x 10 = 70/17 = 4.117 minutes

You can so work just on person B instead

"The whole job" needs 7 minutes.
(10/17) "of the whole job" needs ? minutes

((10/17) / 1 ) x 7 = 70/17 = 4.117 minutes

For kids between year 4-6, this easier method which can be easily illustrated by a diagram would get them through.

 

[jet]

I actually find that far more complicated. At least in the way which I do it, there is a parallel between speed and their rate of cleaning the room.
I am not saying that yours is wrong, just that it took a longer time, and I truthfully got lost reading it.
And I never meant deriving a formula or something. For problems like these, you need to be able to adapt to every one is what I have found, so I didn't try to stress it as the way to tackle every problem. I actually applaud the dynamic mathematician, as they are far more skillful in my eyes then someone who memorises formulas.

 

[oasfree]

I actually find that far more complicated. At least in the way which I do it, there is a parallel between speed and their rate of cleaning the room.
I am not saying that yours is wrong, just that it took a longer time, and I truthfully got lost reading it.
And I never meant deriving a formula or something. For problems like these, you need to be able to adapt to every one is what I have found, so I didn't try to stress it as the way to tackle every problem. I actually applaud the dynamic mathematician, as they are far more skillful in my eyes then someone who memorises formulas.

I think it's relative and hard to judge which way is easier depending on what you are used to. There are many ways to solve same problem. Some ways require knowledge that often get taught in later years. The way you presented actually requires many more steps in between such as addition of fraction, getting common denominator, ... The reason why you got lost reading my method because you were probably not familiar with manipulation ratios this way.

The advantage oft the method I presented is that you can graphically draw it. In fact they often draw a digram to illustrate the thinking to make it possible to teach young kids. I often see this method used in Singaporean tests for kids between grade 5-6. They seem to do tougher math than what kids do in Australia. Not sure if that is better or a bad idea.