Last visit was: 14 Jul 2024, 23:11 It is currently 14 Jul 2024, 23:11
Toolkit
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

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.

# John would have reduced the time it took him to drive from his home to

SORT BY:
Tags:
Show Tags
Hide Tags
Joined: 27 Sep 2015
Posts: 49
Own Kudos [?]: 563 [32]
Given Kudos: 26
GMAT 1: 410 Q33 V13
WE:Management Consulting (Computer Software)
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21835
Own Kudos [?]: 11778 [14]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6805
Own Kudos [?]: 30800 [2]
Given Kudos: 799
General Discussion
SVP
Joined: 20 Mar 2014
Posts: 2359
Own Kudos [?]: 3649 [3]
Given Kudos: 816
Concentration: Finance, Strategy
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
Re: John would have reduced the time it took him to drive from his home to [#permalink]
2
Kudos
1
Bookmarks
RSOHAL wrote:
John would have reduced the time it took him to drive from his home to a certain store by 1/3 if he had increased his average speed by 15 miles per hour. What was John's actual average speed, in miles per hour, when he drove from his home to the store?

(A) 25
(B) 30
(C) 40
(D) 45
(E) 50

Source: GMAT Focus

Let v,t be the original speed and time taken by John

As the total distance (=speed*time) must be the same,

v*t = (2t/3)*(v+15) ---> v=30 miles per hour.

Manager
Joined: 21 Jan 2014
Posts: 88
Own Kudos [?]: 50 [0]
Given Kudos: 46
GMAT 1: 500 Q32 V28
GPA: 4
Re: John would have reduced the time it took him to drive from his home to [#permalink]
Engr2012 wrote:
RSOHAL wrote:
John would have reduced the time it took him to drive from his home to a certain store by 1/3 if he had increased his average speed by 15 miles per hour. What was John's actual average speed, in miles per hour, when he drove from his home to the store?

(A) 25
(B) 30
(C) 40
(D) 45
(E) 50

Source: GMAT Focus

Let v,t be the original speed and time taken by John

As the total distance (=speed*time) must be the same,

v*t = (2t/3)*(v+15) ---> v=30 miles per hour.

I like the way you approached the question.
I tried to solve the question in a similar way, but without success

the new time given is equal to x-1/3, while the distance is the same and the John's rate changed, which is equal to Disatnce/time - 1/3.
In this way I got this equation: x-1/3=D/T-1/3... after that I was stucked.

Where did I fail?
SVP
Joined: 20 Mar 2014
Posts: 2359
Own Kudos [?]: 3649 [1]
Given Kudos: 816
Concentration: Finance, Strategy
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
Re: John would have reduced the time it took him to drive from his home to [#permalink]
1
Kudos
pepo wrote:
Engr2012 wrote:
RSOHAL wrote:
John would have reduced the time it took him to drive from his home to a certain store by 1/3 if he had increased his average speed by 15 miles per hour. What was John's actual average speed, in miles per hour, when he drove from his home to the store?

(A) 25
(B) 30
(C) 40
(D) 45
(E) 50

Source: GMAT Focus

Let v,t be the original speed and time taken by John

As the total distance (=speed*time) must be the same,

v*t = (2t/3)*(v+15) ---> v=30 miles per hour.

I like the way you approached the question.
I tried to solve the question in a similar way, but without success

the new time given is equal to x-1/3, while the distance is the same and the John's rate changed, which is equal to Disatnce/time - 1/3.
In this way I got this equation: x-1/3=D/T-1/3... after that I was stucked.

Where did I fail?

The mistake you are doing is that when you are told that the time is reduced by 1/3 it's not x-1/3 but x-x/3 = 2x/3
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21835
Own Kudos [?]: 11778 [1]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: John would have reduced the time it took him to drive from his home to [#permalink]
1
Kudos
Hi pepo,

In this question, the changes in rate and time are based on 'ratios' (NOT on an absolute number).

For example, if you're traveling 60 miles/hour and you reduce THAT speed by 1/3, the calculation is NOT 60 - 1/3.... it's 60 - (1/3)(60) = 40.

Since most of your other math 'skills' seem fine, this issue is ultimately about your organization and how you take your notes. Instead of just writing down "- 1/3", you should think about what that difference represents (it represents a 1/3 decrease in speed) and add a bit more detail to your work.

GMAT assassins aren't born, they're made,
Rich
SVP
Joined: 26 Mar 2013
Posts: 2456
Own Kudos [?]: 1369 [0]
Given Kudos: 641
Concentration: Operations, Strategy
Schools: Erasmus (II)
John would have reduced the time it took him to drive from his home to [#permalink]
There a re different approaches for the question. Engr2012 & Rich demonstrated great algebraic and logic way.

Another way that we can mix and match between both.

distance is constant. Any decrease in time means increased speed (or vice versa)

So time decreased by 1/3..........>remaining time is 2/3.........> speed is 3/2= V2/V1= (V1+15)/V1 (where V2: new speed & V1:original speed)

TESTing The Answers, it is easily to find that

(30+15)/15=45/30=3/2

Board of Directors
Joined: 17 Jul 2014
Posts: 2145
Own Kudos [?]: 1189 [2]
Given Kudos: 236
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE:General Management (Transportation)
Re: John would have reduced the time it took him to drive from his home to [#permalink]
2
Kudos
suppose r=his rate, t his time, rt = distance traveled
new time 2t/3, new rate r+15, distance is the same = rt.

now, (r+15)* 2t/3 = rt
2rt/3 + 10t = rt - multiply by 3 to get rid of the fractions:
2rt +30t = 3rt
30t = rt | divide by t
30=r.

his rate was 30.
Retired Moderator
Joined: 18 May 2019
Posts: 782
Own Kudos [?]: 1055 [0]
Given Kudos: 101
Re: John would have reduced the time it took him to drive from his home to [#permalink]
This is my approach.
Time (t)= distance(d)/speed(s)
This means t is inversely proportional to speed
In this case the distance is the constant since it’s the same and can be ignored since it will cancel out in the equations.
So we can say that t=1/s ........(a)
Where t is the original time taken by John to travel home at a speed of s

We are told that he can reduce his speed by 1/3 had he increased his average speed by 15mph.

So new time would now be 2t/3 and will correspond to a speed of s+15
Hence 2t/3=1/(s+15)
So t=3/(2(s+15)) ........(b)

equating (a) to (b)

1/s=3/(2s+30)
3s=2s+30
Hence s=30

Posted from my mobile device
Non-Human User
Joined: 09 Sep 2013
Posts: 33971
Own Kudos [?]: 851 [0]
Given Kudos: 0
Re: John would have reduced the time it took him to drive from his home to [#permalink]
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.
Re: John would have reduced the time it took him to drive from his home to [#permalink]
Moderator:
Math Expert
94342 posts