# Thread: Point of No Return (Wrd P)

1. ## Point of No Return (Wrd P)

A plane flying the 3458-mi trip from New York City to London has a 50-mph tailwind. The flight's point of no return is the point at which the flight time required to return to New York is the same as the time required to continue to London. If the speed of the plane in still air is 360 mph, how far is New York from the point of no return?

Can anyone lead me in the right direction with this one? I've been at it for an hour and am brain dead x.x

2. Originally Posted by CODEONE
A plane flying the 3458-mi trip from New York City to London has a 50-mph tailwind. The flight's point of no return is the point at which the flight time required to return to New York is the same as the time required to continue to London. If the speed of the plane in still air is 360 mph, how far is New York from the point of no return?

Can anyone lead me in the right direction with this one? I've been at it for an hour and am brain dead x.x
the 50-mph tail wind means the plane's speed to London is $360 + 50 = 410$ mph and the plane's speed to New York is $360 - 50 = 310$ mph

let $d$ be the distance from New York to the point of no return
then $3458 - d$ is the distance from London to the point of no return.
let $t_L$ be the time to fly to London from the point of no return
let $t_{NY}$ be the time to fly to New York from the point of no return

recall that: $\mbox{Speed } = \frac {\mbox{Distance}}{\mbox{Time}} \implies \mbox{Time } = \frac {\mbox {Distance}}{\mbox{Speed}}$

so, $t_{NY} = \frac d{310}$

and $t_L = \frac {3458 - d}{410}$

since the times from the point of no return are the same, we have:

$\frac d{310} = \frac {3458 - d}{410}$

now solve for $d$

3. ## Ummmmmm NO!!!

Originally Posted by CODEONE
A plane flying the 3458-mi trip from New York City to London has a 50-mph tailwind. The flight's point of no return is the point at which the flight time required to return to New York is the same as the time required to continue to London. If the speed of the plane in still air is 360 mph, how far is New York from the point of no return?

Can anyone lead me in the right direction with this one? I've been at it for an hour and am brain dead x.x

the 50-mph tail wind means the plane's speed to London is mph and the plane's speed to New York is mph

let be the distance from New York to the point of no return
then is the distance from London to the point of no return.
let be the time to fly to London from the point of no return
let be the time to fly to New York from the point of no return

recall that:

so,

and

since the times from the point of no return are the same, we have:

now solve for

Hey i don't usually sign up for forums but i did to message you. I am doing this same problem for my intermediate algebra class, the problem here is probably from the same book in section 8.4, number 31, on pg.586 (Introdoctury and intermediate Algebra by Marvin L. Bittinger, Judith A. Beecher.) CODEONE. Because this math problem is an odd number, they post all the odd answers in the back of the book. My math teacher only assigns us odd problems so we can always double check our answers so we know were using right methods. Anyways i'll get righ to it, the answer for this particular problem according to my test (this is the exact same problem from the text) is "1489mi". I don't know how to come to this answer. After re-reading the problem the answer does make since (seeing as the speed of the plane increases going and decreases on returning). Your explanation for setting up the equation seems plausable but in solving it i get a completely weird answer. I come to 10719.8???? Am i doing something wrong, cuz this problem is killing me, did u make a mistake, please respond!

4. Originally Posted by MyNameisZach
Originally Posted by CODEONE
A plane flying the 3458-mi trip from New York City to London has a 50-mph tailwind. The flight's point of no return is the point at which the flight time required to return to New York is the same as the time required to continue to London. If the speed of the plane in still air is 360 mph, how far is New York from the point of no return?

Can anyone lead me in the right direction with this one? I've been at it for an hour and am brain dead x.x

the 50-mph tail wind means the plane's speed to London is mph and the plane's speed to New York is mph

let be the distance from New York to the point of no return
then is the distance from London to the point of no return.
let be the time to fly to London from the point of no return
let be the time to fly to New York from the point of no return

recall that:

so,

and

since the times from the point of no return are the same, we have:

now solve for

Hey i don't usually sign up for forums but i did to message you. I am doing this same problem for my intermediate algebra class, the problem here is probably from the same book in section 8.4, number 31, on pg.586 (Introdoctury and intermediate Algebra by Marvin L. Bittinger, Judith A. Beecher.) CODEONE. Because this math problem is an odd number, they post all the odd answers in the back of the book. My math teacher only assigns us odd problems so we can always double check our answers so we know were using right methods. Anyways i'll get righ to it, the answer for this particular problem according to my test (this is the exact same problem from the text) is "1489mi". I don't know how to come to this answer. After re-reading the problem the answer does make since (seeing as the speed of the plane increases going and decreases on returning). Your explanation for setting up the equation seems plausable but in solving it i get a completely weird answer. I come to 10719.8???? Am i doing something wrong, cuz this problem is killing me, did u make a mistake, please respond!
Ummmm, YES!!!

i made no mistake, please check your algebra, Zack. my solution gives the distance is 1488.86, which is rounded to 1489, as is in the book. you solved for d incorrectly (which should have been obvious, since if you plug in that d in my equation, you have the left side positive, but the right side negative)

is there anything else you don't understand in my solution?

5. ## Please help me

I still don't see how you get that answer for D with your equation. I cross multiple the two equations left & continually come out with d = 10719.8 which is not the answer. Are you trying to make me look like a fool? Please show me how you get this answer i really want to know, r u a math teacher?

6. Originally Posted by MyNameisZach
I still don't see how you get that answer for D with your equation. I cross multiple the two equations left & continually come out with d = 10719.8 which is not the answer. Are you trying to make me look like a fool? Please show me how you get this answer i really want to know, r u a math teacher?
i am not a math teacher, and i don't even know you, Zach, why would i be interested in making some random guy i met on the internet look like a fool? i merely said you solved for d incorrectly. i figured you made a silly mistake and could correct it. evidently you keep making the same mistake.

there are many ways to solve the equation. for your benefit, i will use your cross-multiplication method.

$\frac d{310} = \frac {3458 - d}{410}$

cross-multiply

$\Rightarrow 410 d = 310(3458 - d)$ .............chances are you made a mistake here and did not distribute the 310 to both terms

$\Rightarrow 410 d = 1071980 - 310d$ ...........add 310d to both sides

$\Rightarrow 720d = 1071980$ ..............divide both sides by 720

$\Rightarrow d = \frac {1071980}{720}$ ..........simplify

$\Rightarrow \boxed{d = 1488.861 \approx 1489}$

7. ## Suddenly i see

Omg i was making the stupidest mistake i feel like an idiot, thanks for taking the time to answer. can i message you if i have trouble in the future?

8. Originally Posted by MyNameisZach
Omg i was making the stupidest mistake i feel like an idiot, thanks for taking the time to answer. can i message you if i have trouble in the future?
it is best (for you) to post your questions here in the forum. i'll help you out if i'm around and no one else does

9. ## <3

Thanks, i love you

### how to solve for the point of no return for a plane taking off

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