It is currently 12 Aug 2020, 10:10

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

 Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Senior Manager
Joined: 20 May 2014
Posts: 283
Followers: 23

Kudos [?]: 61 [2] , given: 220

A transcontinental jet travels at a rate of x – 100 mph with [#permalink]  01 Oct 2017, 04:30
2
This post received
KUDOS
00:00

Question Stats:

70% (03:21) correct 30% (03:45) wrong based on 20 sessions
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.

Kudos for correct solution.
[Reveal] Spoiler: OA
VP
Joined: 20 Apr 2016
Posts: 1292
WE: Engineering (Energy and Utilities)
Followers: 20

Kudos [?]: 1263 [1] , given: 246

Re: A transcontinental jet travels at a rate of x – 100 mph with [#permalink]  01 Oct 2017, 06:37
1
This post received
KUDOS
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.

Kudos for correct solution.

quick way is to plug the values,

Let take option C

therefore tailwind rate is = x+100 = 600

Now putting the values in $$speed= \frac{dist}{time}$$ formula

we get $$600 = \frac{3200}{time}$$

or time = 5 hr 20 min

now calculating for headwind we have

since we have taken x+100 = 600 or x= 500

therefore headwind speed = x-100 = 500-100= 400

Putting the value in $$speed = \frac{distance}{time}$$
we get $$time = \frac{3200}{400} = 8 hour$$ which exactly 2 hr 40 mins addition to tailwind. So ans is 600.

When putting the values in the equation it is better to choose from option C and then depending on the result we can go above C or below C.
_________________

If you found this post useful, please let me know by pressing the Kudos Button

Rules for Posting

Got 20 Kudos? You can get Free GRE Prep Club Tests

GRE Prep Club Members of the Month:TOP 10 members of the month with highest kudos receive access to 3 months GRE Prep Club tests

Intern
Joined: 12 Oct 2017
Posts: 23
Followers: 0

Kudos [?]: 13 [2] , given: 3

Re: A transcontinental jet travels at a rate of x – 100 mph with [#permalink]  13 Oct 2017, 05:16
2
This post received
KUDOS
3200 / (x-100) - 3200 / (x+100) = 8/3 (Hrs)

By Solving this equation we can get the answer
Intern
Joined: 12 Oct 2017
Posts: 23
Followers: 0

Kudos [?]: 13 [1] , given: 3

Re: A transcontinental jet travels at a rate of x – 100 mph with [#permalink]  13 Oct 2017, 05:20
1
This post received
KUDOS
Another method is by puting the values of X As 500,540,600,720

First put the value of x as 500
Speeds are 400 and 600
time taken to travel 3200 is 8 hrs and 5 hrs 20 mins.
Difference in time is 2 hrs 40 min as given in the problem
so speed with tailwind is x+100 = 500+100 = 6

This will definately save time.

if the 500 does not work go with the choice 600 as it is easy to eliminate this choice first
Sherpa Prep Representative
Joined: 15 Jan 2018
Posts: 147
GMAT 1: Q V
Followers: 7

Kudos [?]: 236 [0], given: 0

Re: A transcontinental jet travels at a rate of x – 100 mph with [#permalink]  05 Apr 2018, 11:54
Expert's post
Pranab01's solution, by plugging in answers, is the best way. But I wanted to point out why the algebra is a bad idea.

ALGEBRAIC METHOD:

If you decide to solve using algebra, you'd make a couple of equations using the rate formula: RT = D

(x + 100)t = 3200
and
(x - 100)(t + 2 2/3) = 3200

If you ever have two equations in which two variables are multiplied, and then a bit has been added or subtracted and they're multiplied again, this will turn into a quadratic equation. And not a nice one. Quadratics can be solved of course, but hidden quadratics like this usually can't be solved very quickly because there will be like 15 steps. So if you ever see any equation like this, go straight to the answer choices! It's guaranteed to be easier.

PLUG IN ANSWERS METHOD:

If you're going to plug in, as pranab01 did, don't just start with A. Usually you want to start with one of the middle answers so that if it's too large, you know to pick a smaller answer. It's also a good idea to try to pick whichever numbers will be easiest to deal with. Since C, 600, fulfills both categories, I'd start with C, and it's probably not a coincidence that C is the correct answer. For details on the plug-in method see pranab01's response.
_________________

-
-
-
-
-

Need help with GRE math? Check out our ground-breaking books and app.

GRE Instructor
Joined: 10 Apr 2015
Posts: 3672
Followers: 142

Kudos [?]: 4236 [0], given: 67

Re: A transcontinental jet travels at a rate of x – 100 mph with [#permalink]  29 Jul 2020, 07:44
Expert's post
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.

Kudos for correct solution.

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
_________________

Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.

Sign up for GRE Question of the Day emails

Re: A transcontinental jet travels at a rate of x – 100 mph with   [#permalink] 29 Jul 2020, 07:44
Display posts from previous: Sort by

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

 Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.