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**+2 **

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

CPhill
Sep 19, 2018

#6**0 **

Replay of invisable posts

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

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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.

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*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!.*

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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