# How do you solve this math problem? Thanks!?

A turbojet flies 50mph faster than an irplane. If a turbojet goes 2000miles in 3hours less time than it takes an airplane to go 28000 miles, find the speed of each plane.

I know the solution should use a quadratic equation, but the equation that i get can't be factored.

Please hep!, thanks!

### 4 Answers

- Anonymous1 decade agoFavorite Answer
I'm going to assume you meant 2800 instead of 28000...

v,j= v,p + 50

v,p = 2800/t

v,j = 2000/(t-3) = 2800/t + 50

2000/(t-3) = (2800 + 50t)/t

2000t = (t-3)(2800 + 50t)

2000t = 2800t + 50t² - 8400 - 150t

2000t = 2650t + 50t² - 8400

50t² + 650t - 8400 = 0

t² + 13t - 168 = 0

t = [-13 ± √(169 + 672)] / 2 = 8

v,p = 2800/8 = 350 mph

v,j = 2000/5 = 400 mph

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- 1 decade ago
i solved it.. i also obtained an unfactorable quadratic equation, and its your job to check to see if my answers are correct

TO SOLVE:

Let a be the speed of the airplane and t be the speed of the turbojet.

t = 50 + a

t = 2000/((28000/a) - 3)

Note that the 28000/a is the distance divided by the speed of the airplane, thus that is the time of the airplane. So the time of the turbojet will be the time of the airplane minus 3 as the question states..

and t the speed of the turbojet becomes 28000 divided by the time..

Simplifying, we obtain

t = 2000/((28000 - 3a)/a), t = 2000a/(28000-3a)

From the first statement, t = 50 +a, so a = t - 50, so replace t-50 into any place you see a, we obtain

t = 2000(t-50)/(28000-3(t-50))

t = (2000t-100000)/(28000-3t+150)

t = (2000t-100000)/(28150-3t)

28150t-3t^2 = 2000t-100000

26150t-3t^2=-100000

3t^2 - 26150 -100000 = 0

Now solve using quadratic equation

I obtained 8720.48908mph as t and discarded the other value since speed cant be negative.

a = t-50 = 8720.48908-50 = 8670.48908mph..

thats what i obtained but i might have being wrong somewhere..

hope this helps

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- Anonymous1 decade ago
let x be the speed of the airplane

the speed of the turbojet is x+50

2000/(x+50)=28000/x+3

2000/(x+50)=(28000+3x)/x

2000x=(28000+3x)(x+50)

2000x=28000x+1400000+3x^2+150x

3x^2+26150x+1400000=0

im not sure.. i might have made some calculation mistakes but is this the equation you got?

you can also try using the quadratic formula

here: http://argyll.epsb.ca/jreed/math20p/quadraticFunct...

you can just substitute the a and b and c values to find the x value

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- YumanLv 41 decade ago
Let's define some variables and faithfully translate the problem statements into equations from English.

Vt: speed of turbojet

Va: speed of airplane

T: time for an airplane to go 28000 miles

Recall V = Distance/Time

T = D/V

Vt = Va +50

T = 28000/Va

2000/Vt = T-3

Eliminating T gives

2000/Vt = 28000/Va -3

which is the same as

2000Va = 28000Vt -VaVt

= 28000(Va+50) -Va(Va+50)

Then use this http://mathworld.wolfram.com/QuadraticEquation.htm...

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