Finding the speed of an aeroplane

[wrightarya]

question is attached.
the answer at the back of the book is 553.6 kmph

this is for my maths homework and I am stuck on this question.:(

 

[Prove It]

question is attached.
the answer at the back of the book is 553.6 kmph

this is for my maths homework and I am stuck on this question.:(

What have you tried so far?

 

[wrightarya]

If the speed is x km/h then the time taken is 1000/x hours.

If the speed is x-120 then the time taken is 1000/x hours and this is equal to the other time plus 0.5 hours.

i don't know how to form an equation =/

 

[Prove It]

If the speed is x km/h then the time taken is 1000/x hours.

If the speed is x-120 then the time taken is 1000/x hours and this is equal to the other time plus 0.5 hours.

i don't know how to form an equation =/

Actually if the speed is (x - 120) then the speed is 1000/(x - 120).

Now as you have stated, this is equal to the other time plus half an hour, so

$\displaystyle \begin{align*} \frac{1000}{x - 120} &= \frac{1000}{x} + \frac{1}{2} \end{align*}$

Can you now solve for x?

 

[wrightarya]

Actually if the speed is (x - 120) then the speed is 1000/(x - 120).

Now as you have stated, this is equal to the other time plus half an hour, so

$\displaystyle \begin{align*} \frac{1000}{x - 120} &= \frac{1000}{x} + \frac{1}{2} \end{align*}$

Can you now solve for x?

i tried solving it like this:

1000/x-120 = 2000 + x
1000= (2000+x) (x-120)
1000= x^2 + 1880x - 240000
= x^2 + 1880x - 241000
substituted into quadratic formula
x=120 or -2000

dont know if i did that right, but its not what the answer says in the back of the book...

 

[Prove It]

i tried solving it like this:

1000/x-120 = 2000 + x

No, $\displaystyle \begin{align*} \frac{1000}{x} + \frac{1}{2} \end{align*}$ is not $\displaystyle \begin{align*} 2000 + x \end{align*}$, it's $\displaystyle \begin{align*} \frac{2000 + x}{2x} \end{align*}$, so when you cross multiply you should get

$\displaystyle \begin{align*} \frac{1000}{x - 120} &= \frac{1000}{x} + \frac{1}{2} \\ \frac{1000}{x - 120} &= \frac{2000 + x}{2x} \\ 1000 \left( 2x \right) &= \left( 2000 + x \right) \left( x - 120 \right) \end{align*}$

Go from here...

 

[M R]

If the speed is x km/h then the time taken is 1000/x hours.

If the speed is x-120 then the time taken is 1000/x hours and this is equal to the other time plus 0.5 hours.

i don't know how to form an equation =/

Finding speed of an aeroplane - The Student Room

You almost quoted me correctly. ;)