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# Finding speed of an aeroplane Watch

1. question is attached.
answer in the back of the textbook is 553.6 kmph
dont know how to work it out, help would be so much appreciated!
Attached Images

2. (Original post by wrightarya)
question is attached.
answer in the back of the textbook is 553.6 kmph
dont know how to work it out, help would be so much appreciated!
If the speed is x km/h then the time taken is hours.

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

Write and solve an equation.
3. i tried solving it like this:
1000/x-120 + 1/2= 1000/x
1000/x-120 = 2000 + x
1000= (2000+x) (x-120)
1000= x^2 + 1880x - 240000
= x^2 + 1880x - 241000
x=120 or -2000

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

let d = distance
let t = time
let u = initial speed (what we're after)

then we reduce u by 120km/h and increase t by half an hour

multiply t to get rid of the fraction

divide through by 20

solving the quadratic gets you t = 1.8065 (5 s.f) (I'm discarding the negative result because obviously time cannot be negative)

then we just substitute our t value to get the answer.

Hope that helps.
5. (Original post by The Financier)
Spoiler:
Show

let d = distance
let t = time
let u = initial speed (what we're after)

then we reduce u by 120km/h and increase t by half an hour

multiply t to get rid of the fraction

divide through by 20

solving the quadratic gets you t = 1.8065 (5 s.f) (I'm discarding the negative result because obviously time cannot be negative)

then we just substitute our t value to get the answer.

Hope that helps.
Thank You so so so much!
if you dont mind, i also worked out another way to do it, sort of like how i tried to do it in the previous post.

i did

1000/x-120 = 1000/x + 1/2
1000/x-120 = 2000+x/2x
2000x = (2000+x)(x-120)
and i solved for x which this time (accidentally) gave me x=553.56km/h

im not sure why the 1/2 had to be added on to the 1000/x but not on the 1000/x-120
would you know why this is so?

thanks again
6. (Original post by wrightarya)
i tried solving it like this:
1000/x-120 + 1/2= 1000/x
1000/x-120 = 2000 + x
1000= (2000+x) (x-120)
1000= x^2 + 1880x - 240000
= x^2 + 1880x - 241000
x=120 or -2000

dont know if i did that right, but its not what the answer says in the back of the book...
You have put the on the wrong side of the equation
7. (Original post by The Financier)
..
Please don't post full solutions. It's against the rules of the maths forum plus it would have been much more beneficial to point out the mistake in the OPs working.
8. (Original post by wrightarya)
Thank You so so so much!
if you dont mind, i also worked out another way to do it, sort of like how i tried to do it in the previous post.

i did

1000/x-120 = 1000/x + 1/2
1000/x-120 = 2000+x/2x
2000x = (2000+x)(x-120)
and i solved for x which this time (accidentally) gave me x=553.56km/h

im not sure why the 1/2 had to be added on to the 1000/x but not on the 1000/x-120
would you know why this is so?

thanks again
The 1000/(x-120) time is 0.5 hrs more than the 1000/x time.

So 1000/(x-120) = (1000/x) + 0.5
9. (Original post by notnek)
Please don't post full solutions. It's against the rules of the maths forum plus it would have been much more beneficial to point out the mistake in the OPs working.
My apologies. I thought the spoiler tag would indicate it would be a full solution (and so would be seen as a last resort) and it seemed like it was only just an expansion of what BabyMaths had originally posted. I'll bear this in mind in future.
10. (Original post by notnek)
The 1000/(x-120) time is 0.5 hrs more than the 1000/x time.

So 1000/(x-120) = (1000/x) + 0.5
I have attached a very similar question to the one I originally posted.
and i worked out the solution by making this equation:

40/x = 40/(x+40) + 1/3
and solved for x to get
x= 52.11 which is the correct answer.

im not sure why in this question the 1/3 hour is added on to 40/(x+40)
but for the question I originally posted, the 1/2 is added onto the 1000/5 instead of the 1000/(x-120)

could anyone tell me why this is so? thanks
Attached Images

11. (Original post by wrightarya)
I have attached a very similar question to the one I originally posted.
and i worked out the solution by making this equation:

40/x = 40/(x+40) + 1/3
and solved for x to get
x= 52.11 which is the correct answer.

im not sure why in this question the 1/3 hour is added on to 40/(x+40)
but for the question I originally posted, the 1/2 is added onto the 1000/5 instead of the 1000/(x-120)

could anyone tell me why this is so? thanks
The main difference here is that your x in the first question is the faster speed and x in the second question is the slower speed.

If in the second question, you called the speed of Jack x instead of Mark then you'll find that your equations for both questions are similar.

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