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

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

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New post 28 Jul 2017, 08:43
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Question Stats:

55% (03:13) correct 45% (03:23) wrong based on 76 sessions

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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.

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

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New post 28 Jul 2017, 11:50
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1
Time to cover the distance with wind is 3200/(x+100)
And time taken to cover against and is 3200/(x-100).
Now the stem says it takes 2 hours and 40 mins more to complete the trip with headwind. So 2 hours and 40 in turn to 8/3 hours.
So the equation is
[3200/(x-100)] -[3200/(x+100)] = 8/3...
Solving we get x=500 which is the speed of jet ad 100 is the speed of wind.
Combined it's 600.
Answer is C

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

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New post 28 Jul 2017, 19:38
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.

I backsolved. I was taking too long to find the equations.

Start with Answer C, 500

Difference in time should be 2 hours 40 minutes = 2\(\frac{2}{3}\) = \(\frac{8}{3}\) hours

1. Find tailwind time from \(D/r\)

TW time is \(\frac{3200}{600}\) = \(\frac{32}{6}\) = \(\frac{16}{3}\) hours

2. Find headwind rate in order to find headwind time

Tailwind rate is 500 = x + 100, x = 400
Headwind rate is x - 100 = 300

3. Find headwind time

HW time is \(\frac{3200}{400}\) = \(\frac{32}{4}\) = 8 hours

4. Difference in time?

(8 -\(\frac{16}{3}\))=(\(\frac{24- 18}{3}\)) = \(\frac{8}{3}\) hours. Correct.

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

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New post 28 Jul 2017, 23:03
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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

Answer C

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

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New post 07 Sep 2018, 07:21
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