SOLUTION: It takes an airplane 4 hours to travel 1000 miles with a tail wind. It takes the plane 5 hours to make the return trip against the wind? What is the speed of the plane and the wind

Question 1167546: It takes an airplane 4 hours to travel 1000 miles with a tail wind. It takes the plane 5 hours to make the return trip against the wind? What is the speed of the plane and the wind?
Found 2 solutions by math_helper, ikleyn:
Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!
It just "feels" like the airplane travels 225mi/hr and the wind is 25mi/hr.
----

With the wind: 1000mi / 4hrs = 250mi/hr
Against the wind: 1000mi / 5hrs = 200mi/hr

225mi/hr is right in the middle, and that is the airplane's speed in still air.
That leaves the wind at 25mi/hr to make up the difference.

Algebraic solution:
Let a = speed of airplane in still air
w = wind speed

(1) (a+w)*4 = 1000 --> 4a + 4w = 1000
(2) (a-w)*5 = 1000 --> 5a - 5w = 1000
Multiply the first equation by 5/4:
(1') 5a + 5w = 1250
(2) 5a - 5w = 1000
Add (1') and (2): 10a = 2250 --> a = 225 (airplane speed 225mi/hr)
Plug this value into (1): 4(225) + 4w = 1000 --> 4w = 100 --> w = 25
(wind speed is 25mi/hr)

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

Let u be the speed of the plane at no wind, and let v be the speed of the wind. The effective speed with the wind u + v = 1000/4 = 250 mph (1) The effective speed against the wind u - v = 1000/5 = 200 mph (2) Add equations (1) and (2) 2u = 450 u = 450/2 = 225 mph Next, from equation (1) v = 250 - 225 = 25 mph. ANSWER. The speed of the plane at no wind is 225 mph. The speed of the wind is 25 mph.

Solved.

---------------

It is a typical "tailwind and headwind" word problem.

See the lessons
    - Wind and Current problems
    - Wind and Current problems solvable by quadratic equations
    - Selected problems from the archive on a plane flying with and against the wind
in this site, where you will find other similar solved problems with detailed explanations.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the section "Word problems", the topic "Travel and Distance problems".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.

RELATED QUESTIONS
An airplane takes 3 hours to travel a distance of 2160 miles with the wind. The return... (answered by mananth)
An airplane takes 3 hours to travel a distance of 2160 miles with the wind. The return... (answered by mananth)
An airplane takes 3 hours to travel a distance of 1680 miles with the wind. The return... (answered by lwsshak3)
An airplane takes 3 hours to travel a distance of 1680 miles with the wind. The return... (answered by mananth)
an airplane takes 5 hours to travel a distance of 4200 miles with the wind. The return... (answered by Boreal)
Please help me with this problem: An airplane takes 5 hours to travel a distance of... (answered by Paul)
An airplane, traveling with a tail wind, travels 1000 miles in 2 hours. The return trip, (answered by Alan3354)
An airplane takes hours to travel a distance of against the wind. The return trip takes (answered by stanbon)
An airplane traveling with the wind flies 450 miles in 2 hours. On the return trip, the... (answered by ankor@dixie-net.com)