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

Question

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.

(A) 500

(B) 540

(C) 600

(D) 720

(E) Cannot be determined by the information given.

kumarparitosh123 · Answer

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
   -  = 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

Sent from my Lenovo TAB S8-50LC using  GMAT Club Forum mobile app

generis · Answer

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

shashankism · Answer

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

BrentGMATPrepNow · Answer

Let's start with a  "word equation"

(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

Answer: C

Cheers,
Brent

EgmatQuantExpert · Answer

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

Correct Answer: Option C

amoldhawan · Answer

Hi all, this question took me 3:20 minutes to solve, should i be worried?

ScottTargetTestPrep · Answer

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.

Answer: C

Fdambro294 · Answer

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

kajaldaryani46 · Answer

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

Regor60 · Answer

Your interpretation is correct because this is a poorly worded question

saynchalk · Answer

They didn't mention whether it's 2 hours 40 minutes more than tailwind speed or normal speed.

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

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