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**Deon588****Member**- Registered: 2011-05-02
- Posts: 68

Hi all. I can't think of any other way to do this problem any ideas would be much apreciated.

A bus travels 200km at a constant speed a car traveling 10km/h faster than the bus completes the same distance in 1 hour less than the bus, how many hours does the bus take to travel the 200km?

When cross multiplying x seems to cancel out.

Thanks a lot in advance

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,323

hi Deon588,

multiply all the terms by the product of the denominators:

The fractions now 'cancel out' and you are left with a quadratic.

Bob

*Last edited by bob bundy (2011-09-29 06:00:56)*

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**Hixy****Member**- Registered: 2011-09-24
- Posts: 15

Steps:

1. Dissect the problem and extract the important information from each sentence (this is actually two steps). This could be done as follows (some parts are underlined to add emphasis):

"A bus travels 200 km at constant speed":

"A car traveling 10 km/h faster than the bus completes the same distance in 1 hour less than the bus."

2. Set up equations:

For the bus:

For the car:

3. Solve the equations.

*Last edited by Hixy (2011-09-29 06:04:16)*

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,323

hi Hixy,

Yes, but look at the OP. Your equations are the same with v instead of x.

Deon588's problem was in not multiplying out correctly so when the 200x (v) terms cancel there's no x (v) left.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**Deon588****Member**- Registered: 2011-05-02
- Posts: 68

Thanks a lot Hixy works out fine now. Bob am I aloud to multiply the

by (x+10) as well? I'm asking as it's already the denominator of that term?

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,323

hi Deon588

When you have an equation with fractions, it is usually best to get rid of the fractions before any other simplifying.

Consider this non algebraic example first.

Check you agree that this is numerically correct.

Now multiply every fraction by 6.

Now cancel to simplify

OK it works.

So do the same to your expression.

Firstly, multiply every term by x.(x+10)

Then, cancel the x in the first term and the (x+10) in the second to leave

Now you can multiply out the brackets. Yes, the 200x does cancel but there is still a term with x in it.

This simplifies to a quadratic equation which factorises fairly easily. One answer is negative so you can reject it as not possible for this problem. The other answer is the one you want.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**Deon588****Member**- Registered: 2011-05-02
- Posts: 68

Bob thanks again, you really have a talent for making things which seem complicated totally understandable I never thought of handling these fractions the same way as fractions without variables.

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,323

hi Deon588,

Thanks for the nice comments. I am a retired maths teacher, so that may explain it.

I tell my students: "The rules of algebra are just the rules of arithmetic. If you are stuck with all those xs, try it with numbers first."

This often helps.

At the end, did you put your value for x back into the problem, to see if it worked?

That's another thing I tell my students.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,037

hi bob

i didn't know that you are retired.from your posts i got that you still teach.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,323

hi Stefy,

No. Definitely retired from earning money from teaching. But if you count what I do here, then I'm still at it!

And enjoying it! :)

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,037

hi

i'm sure you do.do you do private lessons or are you absolutely out of teaching?

just a question.can i consider you to be my friend?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,323

No private lessons.

can i consider you to be my friend?

Well yes, I'd be honoured to be considered your friend!

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,037

thanks!!!

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**Deon588****Member**- Registered: 2011-05-02
- Posts: 68

Yes I did for the next question I had to find the car's time and it worked perfectly

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**reconsideryouranswer****Member**- Registered: 2011-05-11
- Posts: 171

bob bundy wrote:

Firstly, multiply every term by x.(x+10)

Then, cancel the x in the first term and the (x+10) in the second to leave

Deon588,

but don't use decimal points as above to multiply. Even if they *were* to

mean multiplication, then they would be redundant. Use grouping

symbols instead.

Just as 3.4 equals 3 and four-tenths, it does not equal

And you would not type 200.x to be the equivalent of 200 multiplied by x,

because 200x means 200 multiplied by x.

Then, cancel the x in the first term and the (x+10) in the second to leave

Signature line:

I wish a had a more interesting signature line.

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**Au101****Member**- Registered: 2010-12-01
- Posts: 353

I think what bob bundy was going for is the 'interpunct' symbol, as it is known in written languages, i.e.

Which is the chain rule. Certainly in vector calculus, to represent the scalar product, this must be used and it is eminently possible to use it for multiplication. It also helps separate the parts of bob bundy's multiplication for didactic purposes elegantly. By the way, bob bundy, the LaTeX for that symbol is \cdot - you may find it helpful in future .

*Last edited by Au101 (2011-09-30 23:28:36)*

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,323

hi Au101

Thanks for the dot. I'll use it in honour of you!

Maybe it's my age, but over the time I've met and done maths, I've seen lots of different ways of doing the same thing.

eg. 'j' used to be used instead of 'i' in complex number theory. Since 'j' is usually used for a unit vector in the 'up' direction, there is a certain logic to this. Newton's way for writing calculus was different from the Leibniz notation we use today.

There's nothing wrong with using a new notation as long as it's clear and doesn't confuse. As far as I know the only reason for not using an x for 'times' in algebra is to avoid any confusion with the variable *x* and it is often replaced with a dot.

When I'm first introducing algebraic powers I will deliberately do this:

I'm careful to write my x with a curl and my times straight. My classes can then appreciate (i) why powers are a useful abbreviation for a long_hand product and why it's best to leave out the times signs altogether. I'd rather my classes understood the reason for something, than just did it blindly!

For me, the key test is " does the student undersatnd what they are doing now?"

That's why I am heartened by this comment from Deon588:

Bob thanks again, you really have a talent for making things which seem complicated totally understandable

I must be doing something right!

Bob

*Last edited by bob bundy (2011-10-01 01:29:09)*

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**Au101****Member**- Registered: 2010-12-01
- Posts: 353

As it happens, j is still used to represent the imaginary unit in electrical engineering - where i could easily be confused with the denotation of current.

Also, I completely agree with bob - clarity is what matters - as long as everybody understands it, then it's perfectly acceptable. I would concede, however, that the easiest way to make sure that this is the case is consistency of use, which, I think, is what standardisation of notation is generally aimed at.

*Last edited by Au101 (2011-10-01 04:49:41)*

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**Deon588****Member**- Registered: 2011-05-02
- Posts: 68

Hi. I just came back to this post to check my method for a simular problem and noticed the new posts. Consideryouranswer in South Africa we use a , to represent a decimal so the way Bob did it works perfectly for me. Here 3.4 is always 3*4 and 3,4 is the decimal

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**Deon588****Member**- Registered: 2011-05-02
- Posts: 68

We also write coordinates on the cartetian plane as (x;y) and not (x,y)

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