# Application of Quadratic Functions that involve finding equation

1. May 21, 2016

### Evangeline101

1. The problem statement, all variables and given/known data

2. Relevant equations
none

3. The attempt at a solution

Is this correct?

Thanks.

2. May 21, 2016

### SammyS

Staff Emeritus

There are errors in your work starting with the table.

If x is the speed from Tokyo to Bangkok then reducing that by 200 gives a speed of x - 200 from Bangkok to Tokyo. Etc.

3. May 21, 2016

### Ray Vickson

Plug it in and see if it works.

4. May 22, 2016

### Evangeline101

I understand where I made the error, the return trip speed decreased by 200 km/h, so it should have been (x-200) not (x+200), so I have corrected my answer:

Thanks for the help! :)

5. May 22, 2016

### SammyS

Staff Emeritus
There's still a problem, x is the Tokyo to Bangkok speed. That can't be 600mph. 600 - 200 is 400, and that doesn't work out.

So, where is the problem?

You made a couple of errors.

Sign errors in going from
$-960000=2x^2-400x$​
to
$2x^2+400x-960000= 0$​
It should be
$2x^2-400x+960000= 0$​
But there is no real solution to that.

The problem is that it's the Tokyo to Bangkok time that's smaller, because the speed is greater. When you subtract to get 2 hours, you need to subtract in the opposite order.

6. May 22, 2016

### Evangeline101

I tried doing it this way, but as you said there is no real solution.

I don't understand what you mean, can you please explain?

7. May 22, 2016

### SammyS

Staff Emeritus
If x > 200, then
$\displaystyle \frac{4800}{x-200}>\frac{4800}{x}$​
.

8. May 23, 2016

### Evangeline101

So even if I switch these two, can I not get the same answer I had originally? How does switching the two help with the answer to the problem? or is it just the proper way to write it?

9. May 23, 2016

### SammyS

Staff Emeritus
It's what is needed of you want to make everything consistent.

As I stated in my first reply, the answer you gave for the time from Bangkok to Tokyo was correct. (600 km/hr)

But you had a number of inconsistencies.

You should get x = 800. Then x- 200 = 600, the answer.

Last edited: May 23, 2016
10. May 23, 2016

### Evangeline101

So like this:

11. May 23, 2016

### SammyS

Staff Emeritus
No.Not like that.
The first three lines are correct.

After that, there are at least two Algebra mistakes.

As I stated in my previous post:

12. May 24, 2016

### Evangeline101

This is an example from my lesson that I have been using as a reference to solve my problem:

13. May 24, 2016

### SammyS

Staff Emeritus
Right. And they did not make algebra mistakes. You did.

So (carefully) redo your algebra, starting at the third line of the following (from post #10), which is the last line that's correct.

14. May 24, 2016

### Evangeline101

4800x - 4800x + 960 000 = 2x2 - 400x (960 000 is positive because I multiplied -4800 and -200)

960 000 = 2x2 - 400x (Now I move 960 000 to the right side and it becomes -960 000)

2x2 - 400x - 960 000 = 0

x2 - 200x - 480 000 = 0

(x+600) (x-800)

x= -600 or x = 800

Does this make more sense? did I fix the algebra errors? if not please show me where I made errors.

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15. May 24, 2016

### SammyS

Staff Emeritus
Yes. That looks to be correct.

16. May 24, 2016

### Evangeline101

Okay, so does that make the speed from Bangkok to Tokyo 800 km/h instead of 600 km/h since it is positive?

17. May 24, 2016

### Evangeline101

So since x = 800, we need to solve for the jets's speed from Bangkok to Tokyo, so (like you said) sub x = 800 into x- 200, which gives:
800 - 200 = 600 km/h

So the jet's speed from Bangkok to Tokyo is 600 km/h.

18. May 24, 2016

### Evangeline101

Thanks for the help, I really appreciate it :)