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
Can some experts show me the formula on how to solve it?
OA B
John would have reduced the time it took him to drive
This topic has expert replies
-
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
To reduce the time by 1/3 = to take 2/3 his actual time.lheiannie07 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
Time and rate have a RECIPROCAL RELATIONSHIP.
To take 2/3 his actual time, John must travel at 3/2 his actual speed.
Since 3/2 his actual speed increases the speed by 15 miles per hour, we get:
(3/2)s = s + 15
3s = 2s + 30
s = 30.
The correct answer is B.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Let's start with a word equation:lheiannie07 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
(John's travel time at faster speed) = 2/3(John's regular travel time)
Let r = John's regular speed
So, r+15 = John's faster speed
Let d = the distance traveled at regular speed
So d = the distance traveled at regular speed
time = distance/speed
So, we get: d/(r + 15) = (2/3)(d/r)
Rewrite as: d/(r + 15)= 2d/3r
Cross multiply: (d)(3r) = 2d(r + 15)
Expand: 3rd = 2rd + 30d
Rearrange to get: rd = 30d
Divide both sides by d to get: r = 30
Answer: B
Cheers,
Brent
-
- Senior | Next Rank: 100 Posts
- Posts: 94
- Joined: Tue Dec 16, 2014 9:50 am
- Location: London, UK
- Thanked: 2 times
- Followed by:4 members
- GMAT Score:770
S = Speedlheiannie07 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
Can some experts show me the formula on how to solve it?
OA B
D = Distance
T = Time
We know that S = D/T
From the question we know that S + 15 = D/(2/3)T (if the speed goes up by 15, the time is cut by a third)
S + 15 = D/(2/3)T
S + 15 = (3/2)(D/T)
S + 15 = (3/2)(S) <--- S = D/T
15 = (1/2)S
S = 30
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7243
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
We can let John's speed from his home to the store = r and his time = t. Thus, we have:lheiannie07 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
rt = (r + 15)(2/3)t
r = (r + 15)(2/3)
3r = 2r + 30
r = 30
Answer: B
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi lheiannie07,
We're told that 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. We're asked for John's actual average speed, in miles per hour, when he drove from his home to the store. This question can be solved by TESTing THE ANSWERS (with a little TESTing VALUES thrown in).
We're never told what the distance traveled is, so we can TEST any Value we choose. In addition, it's interesting that increasing his speed by 15 miles/hour would lead to an exact 1/3 decrease in time. Usually, numbers don't 'interact' so nicely (and you end up with weird fractions); here though, the 1/3 decrease heavily implies that John's current speed is some multiple of 15 (so that when we add 15 to that number, we're increasing by a 'nice' percentage).
Let's TEST Answer B: 30 miles/hour
IF.... John travels 30 miles at 30 miles/hour, then the travel time will be 1 hour
increasing that speed by 15 miles/hour would have John traveling 30 miles at 45 miles/hour, so the travel time will be 2/3 of an hour.
This is a decrease of exactly 1/3, which matches what we were told - so this MUST be the answer.
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
We're told that 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. We're asked for John's actual average speed, in miles per hour, when he drove from his home to the store. This question can be solved by TESTing THE ANSWERS (with a little TESTing VALUES thrown in).
We're never told what the distance traveled is, so we can TEST any Value we choose. In addition, it's interesting that increasing his speed by 15 miles/hour would lead to an exact 1/3 decrease in time. Usually, numbers don't 'interact' so nicely (and you end up with weird fractions); here though, the 1/3 decrease heavily implies that John's current speed is some multiple of 15 (so that when we add 15 to that number, we're increasing by a 'nice' percentage).
Let's TEST Answer B: 30 miles/hour
IF.... John travels 30 miles at 30 miles/hour, then the travel time will be 1 hour
increasing that speed by 15 miles/hour would have John traveling 30 miles at 45 miles/hour, so the travel time will be 2/3 of an hour.
This is a decrease of exactly 1/3, which matches what we were told - so this MUST be the answer.
Final Answer: B
GMAT assassins aren't born, they're made,
Rich