Question 1196115: Flying against the wind, a jet travels 3600 miles in 4 hours. Flying with the wind, the same jet travels 7980 miles in 7 hours. What is the rate of the jet in still air and what is the rate of the wind?
Found 3 solutions by josgarithmetic, ikleyn, Alan3354:
Answer by josgarithmetic(39618)   (Show Source):
Answer by ikleyn(52794)  (Show Source):
You can put this solution on YOUR website! .
Flying against the wind, a jet travels 3600 miles in 4 hours.
Flying with the wind, the same jet travels 7980 miles in 7 hours.
What is the rate of the jet in still air and what is the rate of the wind?
~~~~~~~~~~~~~~~~
Flying against the wind, the jet' speed relative the earth surface is
 = 900 miles per hour.
Flying with the wind, the jet' speed relative the earth surface is
 = 1140 miles per hour.
Let "u" be the jet' speed in still air and let "v" be the rate of the wind.
Then we have this system of equations
u + v = 1140 (1)
u - v = 900 (2)
Find "u" by adding equations (1) and (2)
2u = 1140+900 = 2040, u = 2040/2 = 1020.
Find "v" by subtracting equation (2) from equation (1)
v - (-v) = 1140-900, 2v = 240, v = 240/2 = 120.
ANSWER. The jet' speed in still air is 1020 miles per hour.
The rate of the wind is 120 miles per hour.
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.
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! That's a fast jet.
==========
What is the rate of the jet in still air and what is the rate of the wind?
The terms are AIRSPEED and WINDSPEED.
GROUNDSPEED is another term.
|
|
|
