Quadratics and rates help

[luken93]

Hi, can't seem to do this question:
10 A bus is due to reach its destination 75 km away at a certain time. The bus usually travels with an average speed of x km/h. Its start is delayed by 18 minutes but, by increasing its average speed by 12.5 km/h, the driver arrives on time.
a) Find x.
b) How long did the journey actually take?

I set my equations up as:
(1)
(2)
Subbed 1 into 2 etc but couldn't seem to get an answer. Seeing as there are quite a few questions like this in the chapter, is this the right sort of formula to be using?

[the.watchman]

,    (1) (note, I intend to sub t in, so that x is found first )

Sub (1) into (2):









... etc. etc. (usual quadratic process)

OR

Reject the first sol to get 50

Then sub back in to get the time

[luken93]

aah that was the problem, I was trying to clear all the denominators, i'll see if i can do then next question

[ttn]

Another way that I like to do it is

[luken93]

More questions 

1. A freighter sailing due north at 12 km/h sights a cruiser straight ahead at an unknown distance and speeding due east at unknown speed. After 15 minutes the vessels are 10 km apart and then, 15 minutes later, they are 13 km apart. (Assume both travel at constant speeds.) How far apart are the vessels when the cruiser is due east of the freighter?

2. 14 At first two different pipes running together will fill a tank in minutes. The rate that water runs through each of the pipes is then adjusted. If one pipe, running alone, takes 1 minute less to fill the tank at its new rate, and the other pipe, running alone, takes 2 minutes more to fill the tank at its new rate, then the two running together will fill the
tank in 7 minutes. Find in what time the tank will be filled by each pipe running alone at the new rates.

3. Resolve the following rational expressions into partial fractions.
a)

b)

[ttn]

let x = 3




let x = 4 and sub B in also

[ttn]

then let:
to find
to find
to find


For question 2. I had problems with that qn too lol.
It was solved in: http://vcenotes.com/forum/index.php/topic,24798.0.html
look at reply #3, 7 & 11

[luken93]

i get how you got to there, but where do you go from there?

then let:
to find
to find
to find

are these just random numbers or do you work them out?

For question 2. I had problems with that qn too lol.
It was solved in: http://vcenotes.com/forum/index.php/topic,24798.0.html
look at reply #3, 7 & 11

essentials chapter 6? haha
those tap ones are stupid

[ttn]

then let:
to find
to find
to find

are these just random numbers or do you work them out?

You find a value in which it would cancel out the other two leaving you with only one of , or .

So for the first one, you can see that when you let , it'll cancel out and , leaving you .














now theres the (x+1), so you let x = -1 to make it equal 0.












Then to find B, you can use any value you want as long as it doesn't cancel out B.
So any number besides and .
I just used 0, to try keep the numbers easier to work with.
In this last step, you also have to sub back in your values for and










Hope you understood all that  

For question 2. I had problems with that qn too lol.
It was solved in: http://vcenotes.com/forum/index.php/topic,24798.0.html
look at reply #3, 7 & 11

essentials chapter 6? haha
those tap ones are stupid

yeah lol, hate them...

[luken93]

aah that makes so much more sense now, when i read it in the book they just say "lets sub in x=4" i was like wah???

[luken93]

more questions
Can someone please explain how to do:

[the.watchman]

more questions
Can someone please explain how to do:

Do you mean solve for that equals 0, or just simplify?

If the first, ignore the bottom and solve the top for zero.
If the latter, that is simplified, although you can long divide it:

[luken93]

more questions
Can someone please explain how to do:

express in partial fractions to be exact, but thats the correct answer, as always haha
however, i dont understand how you did it? i understand the first line, where you sort of complete the square for some reason but after that its way over my head?

Do you mean solve for that equals 0, or just simplify?

If the first, ignore the bottom and solve the top for zero.
If the latter, that is simplified, although you can long divide it:

[the.watchman]

Ok, well I've basically just long-divided it:



Then



I hope this made more sense
I think you can use a normal long division approach, but I find keeping it in fraction form easier.

[luken93]

Ok, well I've basically just long-divided it:



Then



I hope this made more sense
I think you can use a normal long division approach, but I find keeping it in fraction form easier.

yeeh the long division is where im getting stuck, havent done it since about primary school hha