SOLUTION: A plane flying the 3020-mile trip from City A to City B has a 60 mph tailwind. The flights point of no return is the point at which the flight time required to return to City A is

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Question 334674: A plane flying the 3020-mile trip from City A to City B has a 60 mph tailwind. The flights point of no return is the point at which the flight time required to return to City A is the same as the time required to continue to City B. If the speed of the plane in still air is 430 mph, how far from City A is the point of no return? I need to translate the problem into a pair of linear equations in two variables.

Ok, I have a line:

3020 miles
City A -------------------------------------------- City B

I know d = rt

and the distance is 3020 miles.

So it is rt = 3020, but with the 60 mph tailwind and 430 mph and all that I am just confused.
Found 2 solutions by stanbon, ankor@dixie-net.com:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A plane flying the 3020-mile trip from City A to City B has a 60 mph tailwind. The flights point of no return is the point at which the flight time required to return to City A is the same as the time required to continue to City B. If the speed of the plane in still air is 430 mph, how far from City A is the point of no return? I need to translate the problem into a pair of linear equations in two variables.
Ok, I have a line:
3020 miles
City A -------------------------------------------- City B
I know d = rt
---
Note: The rates change from "to" to "from":
Let "x" miles from A be the point of no return,
then 3020-x is the remaining distance to B and
"x" is the distance back to A:
-----------
Equation:
time to complete the flight to B with wind = time to return to A against wind
(3020-x)/490 = x/370
370(3020-x) = 490x
370*3020-370x = 490x
370*3020 = 860x
x = 1299.3 miles from A
============================
Cheers,
Stan H.

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
A plane flying the 3020-mile trip from City A to City B has a 60 mph tailwind.
The flights point of no return is the point at which the flight time required
to return to City A is the same as the time required to continue to City B.
If the speed of the plane in still air is 430 mph, how far from City A is the point of no return?
:
Not sure why you need two variables here.
:
>>>>>>>>>>>>60 mph wind>>>>>>>>>>>>>>>
A-------------p-----------------------B
|----------------3020 mi--------------|
:
Let p = the distance from A to the point of no return
then
(3020-p) = the distance from B to the point of no return
:
430 + 60 = 490 mph; effective speed with the wind (continue to B)
and
430 - 60 = 370 mph; effective speed against the wind (return to A)
:
Write a time equation, Time = dist/speed
:
Time to return to A = Time to continue to B
=
Cross multiply
490p = 370(3020-p)
490p = 1117400 - 370p
490p + 370p = 1117400
860p = 1117400
p =
p = 1299.3 mi from A is the point of no return
:
:
See if this is true, find the time from p to A & B
dist to B = 3020 - 1299.3 = 1720.7
1299.3/370 = 3.51 hrs back to A
1720.7/490 = 3.51 hrs to B