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## #1 2005-03-27 16:55:11

sskl
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### help! pls state 1st sentence of equation.

Qn1)
In a class there are 4 more boys than girls. 1/3 of the girls and 7/11 of the boys take the train to school. If half of the class take the train, how many boys and girls are there in the class?

Qn2)
A motorist travels 115 km on an expressway at an average speed of 92km/h and another 45minutes on other roads. If the average speed for his whole journey is 80km/h, how far did he travel on the other roads?

Qn3)
A pool can be filled with water by a large pipe within 6 hours. A smaller pipe will take 9 hours to fill the pool. How long will it take to fill the pool if the two pipes operate together?

Qn4)
Find two consecutive numbers such that 4/7 of the larger exceeds 1/2 of the smaller by 5.
my answer: Let the bigger no. be x.
Let the smaller no. be y.
4/7x - 1/2y = 5

## #2 2005-03-27 17:22:55

MathsIsFun

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### Re: help! pls state 1st sentence of equation.

Nice problems!

Let's look at Q4 first (just for fun):

Your formula looks right. Plus they say that they are consecutive numbers, by which I think they mean that x is 1 bigger than y.

So we have two formulas:

(4/7)x - (1/2)y = 5
x-y=1

So, let's do some substituting. Let's replace y with x-1:

(4/7)x - (1/2)(x-1) = 5

Expand out a bit:

(4/7)x - (1/2)x + 1/2 = 5

(4/7-1/2)x + 1/2 = 5

Multiply the lot by 2 to make it nicer:

(8/7-1)x + 1 = 10
(1/7)x=9

x = 9*7 = 63

Let's see if that all works:

(4/7)x - (1/2)y = (4/7)63 - (1/2)62 = 36 - 31 = 5

Yay!

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

## #3 2005-03-27 17:38:54

MathsIsFun

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### Re: help! pls state 1st sentence of equation.

I will have a go at Q3 now, but then I have to go do something else for a while ...

"A pool can be filled with water by a large pipe within 6 hours. A smaller pipe will take 9 hours to fill the pool. How long will it take to fill the pool if the two pipes operate together?"

Hmmm .. let us imagine that the big pipe can pump 1000 litres an hour. I could say "x" an hour, but let's just try with some real numbers for a change.

So the pool would get 6,000 litres in 6 hours.

Now, the smaller pipe takes 9 hours, so it must be pumping 6,000/9 = 666 litres an hour.

TOGETHER (assuming they still work just as well) they would pump 1,000+666 = 1,666 litres an hour.

So it would take 6,000/1,666 = 3.6 hours

If this is homework, you should use proper algebra, something like:

Let x be the rate of flow of the large pipe.

The rate of flow of the small pipe is (6/9)x

The flow rate together is (1+6/9)x

Now, we know that a flow rate of "x" takes 6 hours, so a flow rate of (1+6/9)x should take 6 / (1+6/9) hours:

Time = 6 / (1+6/9) hours

Multiply top and bottom by 9 to simplify:

Time =  9*6 / 9*(1+6/9) = 9*6 / (9+6) = 54/15 = 3.6

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

## #4 2005-03-27 22:25:07

sskl
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### Re: help! pls state 1st sentence of equation.

now i understand the explanation better.
looking forward to the rest of the qn.
hope to hear from u soon.

## #5 2005-03-28 07:57:13

MathsIsFun

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### Re: help! pls state 1st sentence of equation.

I hope I'm not doing all your homework for you! And wouldn't it be funny if I got one wrong

Qn2)
A motorist travels 115 km on an expressway at an average speed of 92km/h and another 45minutes on other roads. If the average speed for his whole journey is 80km/h, how far did he travel on the other roads?

Let me see ... 115km at 92km/h. How much time is that? 115km/92km/h = 1.25h (1h:15m)

And he spent another 45 minutes, so his whole journey was 2h.

And if his average speed over the 2h was 80, then he must have travelled 2h*80km/h = 160km

And so he must have driven 160-115=45km on the other roads. Or not.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman