GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 20 Nov 2018, 03:43

Close

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • All GMAT Club Tests are Free and open on November 22nd in celebration of Thanksgiving Day!

     November 22, 2018

     November 22, 2018

     10:00 PM PST

     11:00 PM PST

    Mark your calendars - All GMAT Club Tests are free and open November 22nd to celebrate Thanksgiving Day! Access will be available from 0:01 AM to 11:59 PM, Pacific Time (USA)
  • Free lesson on number properties

     November 23, 2018

     November 23, 2018

     10:00 PM PST

     11:00 PM PST

    Practice the one most important Quant section - Integer properties, and rapidly improve your skills.

Rate/Distance/Time question

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Manager
Manager
avatar
Joined: 26 Feb 2015
Posts: 115
Rate/Distance/Time question  [#permalink]

Show Tags

New post 23 Mar 2015, 13:08
1
Hey,

I found this question through Khan Academy, it goes as follows:

"A jogger and a walker set out at 9am from the same point, headed in the same direction. The average speed of the jogger is 1 mph slower than twice the speed of the walker. In two hours, the jogger is 3 miles ahead of the walker. Find the rate of the jogger"

Can someone please explain how I'd go about setting this up, preferably in a "Rate * Time = Distance" chart.

Thanks in advance
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12890
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Rate/Distance/Time question  [#permalink]

Show Tags

New post 23 Mar 2015, 16:30
1
Hi erikvm,

This question relates the speed of the walker to that of the jogger, so we can use 1 variable to refer to both.

Speed of Walker: X miles/hour
Speed of Jogger: (2X-1) miles/hour

Now we can use the distance formula (we were told that the length of time is 2 hours for each person):

(Rate)(Time) = Distance

Walker: (X miles/hour)(2 hours) = 2X miles
Jogger: (2X-1 miles/hour)(2 hours) = (4X - 2) miles

We're also told that, after those 2 hours, the jogger is 3 miles ahead of the walker, so the difference in distance can be represented as.....

(4X - 2) - 2X = 3 miles

Now we simplify....

2X - 2 = 3
2X = 5
X = 2.5

This means that the speed of the Walker is 2.5 miles/hour and the speed of the Jogger is 2(2.5) - 1 = 4 miles/hour

With these numbers, we can actually 'double check' the math....

Walker: (2.5)(2) = 5 miles
Jogger: (4)(2) = 8 miles
Difference = 3 miles, which is a match for what we were told.

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7038
Rate/Distance/Time question  [#permalink]

Show Tags

New post 23 Mar 2015, 17:39
1
erikvm wrote:
Hey,

I found this question through Khan Academy, it goes as follows:

"A jogger and a walker set out at 9am from the same point, headed in the same direction. The average speed of the jogger is 1 mph slower than twice the speed of the walker. In two hours, the jogger is 3 miles ahead of the walker. Find the rate of the jogger"

Can someone please explain how I'd go about setting this up, preferably in a "Rate * Time = Distance" chart.

Thanks in advance


hi erikvm,
as u want the answer in the format "Rate * Time = Distance"..
lets first look at the rate..
let walker(W) speed be x, then jogger(J) speed will be 2x-1.....
now lets see the time , we are talking here about dist in 2 hrs.. so time =2 hrs and distance = 3 miles..
the equation here becomes [(2x-1)-x] *2=3....
2x-2=3... x=5/2...
therefore speed of W=5/2mph and J=4mph({2*5/2}-1)
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Intern
Intern
User avatar
Joined: 01 Apr 2015
Posts: 7
Rate/Distance/Time question  [#permalink]

Show Tags

New post 01 Apr 2015, 23:27
Useful tricks in TSD ...

Apti-Tricks

Walking at 3/4 of his usual speeds, a man reaches his office 10 minutes late. Find his usual time to cover the distance between home and office.
Solution: Usual Time = (Late Time)/(1/(3/4) - 1) = 10/(4/3 - 1)

Running at 4/3 of his usual speeds, a man improves his timing by 10 minutes. Find his usual time to cover the distance.
Solution: Usual Time = (Improved Time)/(1 - 1/(4/3)) = 10/(1- 3/4)

Find more useful tips and tricks here - http://aptidude.com/trickbook
_________________

Founder, aptiDude
"Get useful study materials at aptiStore!"

e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 2203
Re: Rate/Distance/Time question  [#permalink]

Show Tags

New post 17 Apr 2015, 23:23
erikvm wrote:
Hey,

I found this question through Khan Academy, it goes as follows:

"A jogger and a walker set out at 9am from the same point, headed in the same direction. The average speed of the jogger is 1 mph slower than twice the speed of the walker. In two hours, the jogger is 3 miles ahead of the walker. Find the rate of the jogger"

Can someone please explain how I'd go about setting this up, preferably in a "Rate * Time = Distance" chart.

Thanks in advance


Dear Erik

In Distance-Speed problems, like in most Word Problems, if you're not so sure about how to go setting up the solution, a good first step is Visualization.

Make the given information come alive in a diagram, and often, you'll be able to see (literally!) what your next step should be. :-D

Like, here is a visual representation of the information in this question:

Image

Let's assume the Jogger's speed is J mph and the walker's speed is W mph. They both start from the same point at the same time. So, we show this common starting point with the dotted gray line. Now, 2 hours later, the jogger is 3 miles ahead of the walker. We've shown the snapshot of 2 hours later with the dotted black line.

Now, what does the diagram tell you?

(Distance traveled by Jogger in 2 hours) = (Distance traveled by Walker in 2 hours) + 3

Distance = Speed*Time

So, the above equation can be written as:

J*2 = W*2 + 3 . . . (1)

This is equation 1 between the 2 unknowns. To find a unique value of j, we need another equation.

And that comes from the fact that

Quote:
The average speed of the jogger is 1 mph slower than twice the speed of the walker.


So, the key takeaway of our discussion:

Representing the given information visually is a great first step in Word Problems

Hope this helped! :)

- Japinder
_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8849
Premium Member
Re: Rate/Distance/Time question  [#permalink]

Show Tags

New post 28 Jan 2018, 22:58
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: Rate/Distance/Time question &nbs [#permalink] 28 Jan 2018, 22:58
Display posts from previous: Sort by

Rate/Distance/Time question

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


cron
Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.