College Algebra: Find plane's speed, windspeed, given conditions.

[torielise99]

An airplane encountered a head wind during a flight between Joppetown and Jawsburgh which took 4 hours and 30 minutes. The return flight took 4 hours. If the distance from Joppetown to Jawsburgh is 2500 ​miles, find the airspeed of the plane​ (the speed of the plane in still​ air) and the speed of the​ wind, assuming both remain constant.

The speed of the plane is? The speed of the wind is?

 

[JeffM]

We are a help site, not an answer site.

please show us what you have been able to do on your own so we can see where you are stuck or where you made a mistake.

 

[mmm4444bot]

An airplane encountered a head wind during a flight between Joppetown and Jawsburgh which took 44
hours and 3030
minutes. The return flight took 44
hours. If the distance from Joppetown to Jawsburgh is 25002500
​miles, find the airspeed of the plane​ (the speed of the plane in still​ air) and the speed of the​ wind, assuming both remain constant.

It looks like some numbers are repeated.

With the headwind (flying into the wind), the trip took 44.5 hours. With the tailwind (flying with the wind), the trip took 44 hours. Each trip was 2500 miles. Is that correct?

What have you tried, so far? Where did you get stuck?

If you can't begin, here are some hints.

With a headwind, the speed of a plane is reduced because the air in which the plane is flying is moving "backwards". (Have you ever tried walking down an escalator that's moving upwards? It slows you down!)

We're told that the wind remains constant, so it's a tailwind on the return trip, and the speed of a plane is increased in a tailwind because now the air is carrying the plane along. (While walking up an escalator that's moving upwards, you're moving upwards at a faster speed versus walking up motionless stairs.)

In other words, if symbol r represents the plane's speed without wind and symbol w represents the wind's speed, then we would express the plane's speed in a headwind as (r-w) and in a tailwind as (r+w). :cool:

 

[Dr.Peterson]

An airplane encountered a head wind during a flight between Joppetown and Jawsburgh which took 44
hours and 3030
minutes. The return flight took 44
hours. If the distance from Joppetown to Jawsburgh is 25002500
​miles, find the airspeed of the plane​ (the speed of the plane in still​ air) and the speed of the​ wind, assuming both remain constant.

The speed of the plane is? The speed of the wind is?

Clearly EVERY number has been doubled, probably by pasting from some source that doesn't copy right. The flight took 4 hour and 30 minutes.

I see this question posted on lots of sites, some of them pasted correctly. If the submitter can't take the time even to proofread, much less show any work, we should do the same.

 

[Dr.Peterson]

Ahhhh....I see....
Solution will not be integer speeds.
A distance of 1800 miles instead of 2500 miles
will result in integer speeds.

If you search for the odd city names, you will find that this problem has been submitted to other sites with a variety of numbers, presumably because it comes from software (MyMathLab or equivalent) that varies the numbers. Unless everyone is mistyping it, the program clearly is not attempting to ensure integer speeds, as they would do for some courses (such as one I teach).

 

[mmm4444bot]

Clearly EVERY number has been doubled …

Yup -- clear as muddied water. (Still, I'm a wee bit embarrased.)

As an aside, there are airplanes that fly at speeds much less than 50mph (I've see at least one manufacturer that claimed no stall speed at all), and a wind blowing at 6 inches per second is still a wind.

PS: I agree that students who cannot be bothered to make a reasonable effort to show their attempts or check what they've posted should probably go to "the end of the line".