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A plane flies from Alphaville to Betaville and then back to Alphaville. When there is no wind, the round trip takes 4 hours and 48 minutes, but when there is a wind blowing from Alphaville to Betaville at 100 miles per hour, the trip takes 5 hours. How many miles is the distance from Alphaville to Betaville?

 

Thanks!

HelpPLZ  Sep 19, 2018
 #2
avatar+90023 
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A plane flies from Alphaville to Betaville and then back to Alphaville. When there is no wind, the round trip takes 4 hours and 48 minutes, but when there is a wind blowing from Alphaville to Betaville at 100 miles per hour, the trip takes 5 hours. How many miles is the distance from Alphaville to Betaville?

 

4hrs, 48 min    =  4.8 hrs.

 

Let D be the distance  between the towns, and  let R be the  normal rate of the plane

 

So we have this equation [ with no wind ]

2D / R  =   4.8

Solving for  D  we have that

2D = 4.8R

D =  2.4R    (1)

 

And when the wind is blowing, we have this equation

 

D / (R + 100)  + D / ( R - 100)  =  5     simplify

 

[ D(R - 100) + D(R + 100) ] / [ (R + 100)(R - 100) ]  = 5

 

[ 2DR]  = 5 [ (R + 100) (R - 100) ]       sub  (1)  for D 

 

2 (2.4R)R  =  5 (R^2 - 10000)

 

4.8R^2  = 5R^2  - 50000

 

5R^2 - 4.8R^2 - 50000  = 0

 

.2R^2  - 50000  = 0

 

.2R^2   =  50000

 

R^2  = 50000/ .2   

 

R^2 =  50000 * 10/ 2

 

R^2  = 250,000     take the square root

 

R = 500 

 

And  using (1 )the distance between the towns  is  (2.4)(500) = 1200 miles

 

 

 

cool cool cool

CPhill  Sep 19, 2018
edited by CPhill  Sep 19, 2018
 #5
avatar+144 
+2

Thank You!!

HelpPLZ  Sep 20, 2018
 #6
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Replay of invisable posts

 

Post #1: deleted because it doesn’t make sense.

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

Here’s your deleted post:

 

Let the speed of the plane from A to B = S, then:

Its speed from B to A =S - 100

48/60 =0.8 hours

Distance =Speed x Time

4.8S =D.......................................(1)

5S - 500=D..................................(2)

4.8S =5S - 500

S  = 2,500 mph-which doesn't make sense!!!

Distance =4.8 x 2,500 =12,000 miles.

 

The reason it doesn’t make sense is because you lack the prerequisites.

Study this site. https://www.ixl.com/math/grade-3

It may take a year or more, but it will bring you up to speed.  

 

…Actually, for you, it might take several years.

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

Are you suffering from some sort of mental disorder? You must be! Since you appear to have nothing else to do but keep copies of everything written on this forum? Seek professional help!! Your footprint betrays you!.

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

It only betrays me if you know what the footprint of a gorilla-orangutan hybrid looks like. You are so fucking stupid, it’s hard to believe you would know.

 

I started copying stupid answers after Ginger pointed out that errant math posts, from those who have advanced m o r o n degrees in stupid and dumb, can offer insights into the chaotic thinking process of deranged minds.  

 

You are a textbook case!!

Guest Sep 20, 2018
edited by Guest  Sep 20, 2018

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