Does this solution make sense?

[supernova1203]

The solution is at the bottom you can skip right to it if you like
1. Homework Statement
A jet flew from Tokyo to Bangkok, a distance of 4800 km. On the return trip, the speed was decreased by 200km/h. If the difference in the times of the flights was 2 hours, what was the jet's speed from Bangkok to Tokyo?


2. Homework Equations

Distance=(speed)(time)
Time=Distance/Speed
Speed=Distance/Time

3. The Attempt at a Solution
On sample questions they showed us how to solve a problem like this, i attempted to solve it in a similar manner however as you will see i was unable to

Let x represent speed

D=4800 Speed=? Time =?
----------------------------------------------------------------------------------------
Distance Speed Time
---------------------------------------------------------------------------------------
A to B 4800 x 4800/x (since time = d/s)
Tokyo
to Bangkok
----------------------------------------------------------------------------------------
B to A 4800 (x-200) 4800/(x-200)
Bangkok Since on return
to Tokyo trip speed was
reduced by 200
----------------------------------------------------------------------------------------
Time -2
----------------------------------------------------------------------------------------

4800/x +4800/(x-200)=-2

Lowest common denominator = x(x-200)
Here we multiply everything by x(x-200)

4800/x*x(x-200)+4800/(x-200)*x(x-200)=-2x(x-200)
Here some of the variable cancel out and the calculations are made and we are left
with the end result which is

4800x-960000+4800x=-2x(x-200)
4800x-960000+4800x=-2x^2+400x (On next step the 2x^2 and the right side is moved to
2x^2-400x+4800x-960000+4800x=0 the left side, hence the change in signs)
2x^2-400x+4800x+4800x-960000=0

Basically at this point my calculations got sketchy because there were several ways of going about this problem at this point, also I believe i had made some errors early in my calculations.




*****************************************************************
I was able to solve this however i should give credit where credit is due
I would like to thank:

sjb-2812 (For fixing the -2x^2 to what it should be which is 2x^2 without the negative)

Apphysicist

zgozvrm

Solution

D = distance
S=speed
T=time
d=st
t=d/s
s=d/t

let x represent the speed

(x-200) because on the return trip the speed was reduced by 200

Distance Speed Time

A to B
(Tokyo 4800 x 4800/x
to Bangkok)



B to A 4800 (x-200) 4800/(x-200)
(Bangkok
to Tokyo)

Total 2



4800/(x-200) - 4800/x = 2

LCD is x(x-200)

4800/(x-200)*x(x-200)-4800/x*x(x-200)=2x(x-200)

the two (x-200) cancel out here as well as the 2 x's cancel out



4800x-4800(x-200)=2x(x-200)
4800x-4800x+960000=2x^2-400x
960000=2x^2-400x
=2x^2-400x-960000
2(x^2-200x-480000)
Standard form-------> =(x^2-200x-480000)

a=1
b=-200
c=-480000

Quadratic equation here

-b+-Sqrt b^2-4ac/2a

-b+sqrt b^2-4ac/2a

-(-200) + sqrt (-200)^2-4(1)(-480000)/2(1)

+200 + sqrt 40000-4(-480000)/2

+200 + sqrt 40000 + 1920000/2

+200 + sqrt 1960000/2

200+1400/2

1600/2

x^1=800


x^2

-b-sqrt b^2 - 4ac/2

200-1400/2

-1200/2

=-600

x^2=-600

Since x^2 does not make sense because its a negative, it is logical to conclude the solution is x^1, which is x=800

Therefore the speed of the jet from Bangkok to Tokyo was 800km/h

 

[Doc Al]

You already have a thread going on this problem: https://www.physicsforums.com/showthread.php?p=3052867#post3052867