# algebra

posted by .

An airplane flying with the wind can cover a certain distance in a = 3 hours. The return trip against the wind takes b = 4.5 hours. How fast is the plane and what is the speed of the wind, if the one-way distance is c = 720 miles?

• algebra -

speed of plane in no wind --- x mph
speed of wind ---- y mph

time with the wind = 720/(x+y) = 3
3x + 3y = 720
x + y = 240

time against the wind = 720/(x-y) = 4
4x - 4y = 720
x-y = 180

2x = 420
x = 210
back in x+y=240
210 + y = 240
y = 30

the plane has a speed of 210 mph, and the wind was 30 mph

• algebra -

You are smart! Thanks!

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The text passage contains a mathematical question about an airplane's travel times and speeds with and against the wind. It also provides a solution to the problem.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# algebra

posted by .

An airplane flying with the wind can cover a certain distance in a = 3 hours. The return trip against the wind takes b = 4.5 hours. How fast is the plane and what is the speed of the wind, if the one-way distance is c = 720 miles?

• algebra -

speed of plane in no wind --- x mph
speed of wind ---- y mph

time with the wind = 720/(x+y) = 3
3x + 3y = 720
x + y = 240

time against the wind = 720/(x-y) = 4
4x - 4y = 720
x-y = 180

2x = 420
x = 210
back in x+y=240
210 + y = 240
y = 30

the plane has a speed of 210 mph, and the wind was 30 mph

• algebra -

You are smart! Thanks!

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1. ### 8th Algebra

1) An airplane took 2 hours to fly 600 km against a head wind. The return trip with the wind took 1 2/3 hours. Find the speed of the plane in still air.
2. ### algebra II

An aircraft flew 6 hours with the wind. The return trip took 7 hours against the wind. If the speed of the plane in still air is 276 miles per hour more than the speed of the wind, find the wind speed and the speed of the plane in …
3. ### Math

An airplane flying at a speed of about 100 mph was once overtaken and passed by a flock of sandpipers! Suppose that a flock of these birds can fly at 110 miles per hour with a certain wind and at 90 mph against it. If they fly a certain …
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An airplane takes off from an airport and takes 6.5 hours to fly west (against the wind current) 2600 miles. The return trip (with the wind current) takes 5.2 hours. Find the airspeed and the wind speed.
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Worldwide Airlines flies from Lakeside to Whichitfalls in 4 hours with a tail wind, The return trip against the wind takes 5 hours. Whichitfalls is 5040km from Lakeside. Find the speed of the plane and the velocity of the wind. Would …
6. ### Math

Flying to the wind, an airplane takes 4 hours to go 960 km. The same plane flying with the wind takes only 3 hours to make the same trip. Find the speed of the plane and the speed of the wind. I wasn't here for the lesson from my teacher …
7. ### Algebra

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8. ### Algebra 1

An airplane travels for seven hours with a 60 mph tailwind on the return trip against the same wind it took the plane nine hours find the speed of the plane with no wind.
9. ### Algebra

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10. ### algebra

A man flies a small airplane from Fargo to Bismarck, North Dakota --- a distance of 180 miles. Because he is flying into a head wind, the trip takes him 2 hours. On the way back, the wind is still blowing at the same speed, so the …

More Similar Questions
user
The text passage contains a mathematical question about an airplane's travel times and speeds with and against the wind. It also provides a solution to the problem.

TYPE: SINGLE_QUESTION_WITH_ANSWER