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# A transcontinental jet travels at a rate of x – 100 mph with a headwin

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Re: A transcontinental jet travels at a rate of x – 100 mph with a headwin [#permalink]
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Bunuel wrote:
A transcontinental jet travels at a rate of x – 100 mph with a headwind and x + 100 mph with a tailwind between Wavetown and Urbanio, two cities 3,200 miles apart. If it takes the jet 2 hr 40 minutes longer to complete the trip with a headwind, then what is the jet’s rate flying with a tailwind?

(A) 500

(B) 540

(C) 600

(D) 720

(E) Cannot be determined by the information given.

Time difference between headwind and tailwind = 2 hr 40 min = 2 + 40/60 = 8/3 hour
So, 3200/(x-100) - 3200/(x+100) = 8/3
-> 400 * 200 / (x^2-10000) = 1/3
-> 240000 = x^2 -10000
x^2 = 250000
x = 500

So, Jet's rate flying with a tailwind = 500+ 100 = 600 mph

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Re: A transcontinental jet travels at a rate of x – 100 mph with a headwin [#permalink]
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Bunuel wrote:
A transcontinental jet travels at a rate of x – 100 mph with a headwind and x + 100 mph with a tailwind between Wavetown and Urbanio, two cities 3,200 miles apart. If it takes the jet 2 hr 40 minutes longer to complete the trip with a headwind, then what is the jet’s rate flying with a tailwind?

(A) 500
(B) 540
(C) 600
(D) 720
(E) Cannot be determined by the information given.

(time with headwind) = (time with tailwind) + 2 hours 40 minutes

2 hours 40 minutes = 2 2/3 hours = 8/3 hours
Time = distance/speed

Plug the given values into the word equation to get: 3200/(x – 100) = 3200/(x + 100) + 8/3
Multiply both sides of the equation by 3 to get: 9600/(x – 100) = 9600/(x + 100) + 8
Multiply both sides of the equation by (x – 100) to get: 9600 = 9600(x – 100)/(x + 100) + 8(x – 100)
Multiply both sides of the equation by (x + 100) to get: 9600(x + 100) = 9600(x – 100) + 8(x – 100)(x + 100)
Expand and simplify: 9,600x + 960,000 = 9,600x – 960,000 + 8x² – 80,000
Subtract 9,600x from both sides: 960,000 = –960,000 + 8x² – 80,000
Divide both sides of the equation by 8 to get: 120,000 = –120,000 + x² – 10,000
Simplify right side: 120,000 = x² – 130,000
Add 130,000 to both sides: 250,000 = x²

Solve: x = 500 or x = -500
Since the speed cannot be negative, we know that x = 500

What is the jet’s rate flying with a tailwind?
x + 100 mph = speed with a tailwind
So, the speed with a tailwind = 500 + 100 = 600

Cheers,
Brent
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Re: A transcontinental jet travels at a rate of x – 100 mph with a headwin [#permalink]

Solution

Given
• A transcontinental jet travels at a rate of x – 100 mph with a headwind and x + 100 mph with a tailwind.
• It takes the jet 2 hr 40 minutes longer to complete the trip with a headwind, for a trip between two cities 3,200 miles apart

To Find

• The jet’s rate flying with a tailwind.

Approach and Working Out

• The speed with a tailwind is x + 100 and speed with a headwind is x – 100.
o Time taken with a tailwind = $$\frac{3200}{ {x + 100}}$$.
o Time taken with a headwind =$$\frac{3200}{ {x - 100}}$$.
• Difference in time = 2 hr 40 minutes = 8/3 hours.
• $$\frac{3200}{ {x - 100}}$$ - $$\frac{3200}{ {x + 100}}$$ =$$\frac{8}{3}$$
o Solving we get x = 500
o x + 100 = 600

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Re: A transcontinental jet travels at a rate of x – 100 mph with a headwin [#permalink]
Hi all, this question took me 3:20 minutes to solve, should i be worried?
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Re: A transcontinental jet travels at a rate of x – 100 mph with a headwin [#permalink]
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Bunuel wrote:
A transcontinental jet travels at a rate of x – 100 mph with a headwind and x + 100 mph with a tailwind between Wavetown and Urbanio, two cities 3,200 miles apart. If it takes the jet 2 hr 40 minutes longer to complete the trip with a headwind, then what is the jet’s rate flying with a tailwind?

(A) 500

(B) 540

(C) 600

(D) 720

(E) Cannot be determined by the information given.

Solution:
We can create the equation:

Time traveling headwind = Time traveling tailwind + 2 hours 40 minutes

3,200/(x - 100) = 3,200/(x + 100) + 2 + 40/60

3,200/(x - 100) = 3,200/(x + 100) + 8/3

Multiplying the equation by 3(x - 100)(x + 100), we have:

9,600(x + 100) = 9,600(x - 100) + 8(x - 100)(x + 100)

1,200(x + 100) = 1,200(x - 100) + x^2 - 10,000

1,200x + 120,000 = 1,200x - 120,000 + x^2 - 10,000

x^2 - 250,000 = 0

(x - 500)(x + 500) = 0

x = 500 or x = -500

Since x can’t be negative, x = 500, and the tailwind speed of the jet is x + 100 = 600 mph.

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Re: A transcontinental jet travels at a rate of x – 100 mph with a headwin [#permalink]
amoldhawan wrote:
Hi all, this question took me 3:20 minutes to solve, should i be worried?

with all the Calculations, that may be on the Faster End....

I believe the Goal behind the question was to get you to 'BACK-SOLVE' by Testing the Answers (once you know that you can definitely answer the question)

I rely on Calculations too often as well and need to start Testing Answers more often
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Re: A transcontinental jet travels at a rate of x – 100 mph with a headwin [#permalink]
Ok this might seem a silly Question but I really dont understand why the difference of 2 hr 40 mins is between the speed with a headwind and the speed with a tailwind.

My presumption was that it’d take 2 hrs 40 mins more to travel with a headwind than the regular speed if there was no headwind/ tailwind - and I presumed this would be x.

When I do this, I get x=400 and therefore the speed with tailwind becomes 500. Which is ans option A and clearly, is a trap answer.

Can someone help me understand why do we not consider x instead of x+100?

Posted from my mobile device
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Re: A transcontinental jet travels at a rate of x 100 mph with a headwin [#permalink]
kajaldaryani46 wrote:
Ok this might seem a silly Question but I really dont understand why the difference of 2 hr 40 mins is between the speed with a headwind and the speed with a tailwind.

My presumption was that it’d take 2 hrs 40 mins more to travel with a headwind than the regular speed if there was no headwind/ tailwind - and I presumed this would be x.

When I do this, I get x=400 and therefore the speed with tailwind becomes 500. Which is ans option A and clearly, is a trap answer.

Can someone help me understand why do we not consider x instead of x+100?

Posted from my mobile device

Your interpretation is correct because this is a poorly worded question
Re: A transcontinental jet travels at a rate of x 100 mph with a headwin [#permalink]
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