BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Both car A and car B set out from their original locations..

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 2505
Joined: Sun Oct 15, 2017 1:50 pm
Followed by:6 members

Both car A and car B set out from their original locations..

by BTGmoderatorLU » Thu Apr 05, 2018 5:51 pm
Both car A and car B set out from their original locations at exactly the same time and on exactly the same route. Car A drives from Morse to Houston at an average speed of 65 miles per hour. Car B drives from Houston to Morse at 50 miles per hour, and then immediately returns to Houston at the same speed and on the same route. If car B arrives in Houston 2 hours after car A, how many hours did it take car A to make its trip?

A. 0.50
B. 1.00
C. 1.25
D. 1.33
E. 2.00

The OA is C.

I get the solution in the following way,

Car A: 65m/h
Car B: 50m/h

Houston to morse = m = distance

speed=disttimespeed=disttime

Car A:
65m/h=mt
m=65*t ....equation 1

Car B:
50m/h=2m(t+2)
2m=50*t+50∗2
m=25*t+50....equation 2

Combining equation 1 and 2
65*t=25*t+50
40*t=50
t=5/4
t=1,25.

Please, can anyone explain another way to get the solution? Thanks!
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

by Jay@ManhattanReview » Thu Apr 05, 2018 9:56 pm
BTGmoderatorLU wrote:Both car A and car B set out from their original locations at exactly the same time and on exactly the same route. Car A drives from Morse to Houston at an average speed of 65 miles per hour. Car B drives from Houston to Morse at 50 miles per hour, and then immediately returns to Houston at the same speed and on the same route. If car B arrives in Houston 2 hours after car A, how many hours did it take car A to make its trip?

A. 0.50
B. 1.00
C. 1.25
D. 1.33
E. 2.00

The OA is C.

I get the solution in the following way,

Car A: 65m/h
Car B: 50m/h

Houston to morse = m = distance

speed=disttimespeed=disttime

Car A:
65m/h=m / t
m=65*t ....equation 1

Car B:
50m/h=2m / (t+2)
2m=50*t+50∗2
m=25*t+50....equation 2

Combining equation 1 and 2
65*t=25*t+50
40*t=50
t=5/4
t=1,25.

Please, can anyone explain another way to get the solution? Thanks!
All's fine except a couple of typos. I highlighted them in red.

-Jay
_________________
Manhattan Review GMAT Prep

Locations: Stamford | Istanbul | Evanston | Seoul | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Top
User avatar
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

A and B

by GMATGuruNY » Fri Apr 06, 2018 12:52 am
BTGmoderatorLU wrote:Both car A and car B set out from their original locations at exactly the same time and on exactly the same route. Car A drives from Morse to Houston at an average speed of 65 miles per hour. Car B drives from Houston to Morse at 50 miles per hour, and then immediately returns to Houston at the same speed and on the same route. If car B arrives in Houston 2 hours after car A, how many hours did it take car A to make its trip?

A. 0.50
B. 1.00
C. 1.25
D. 1.33
E. 2.00
Let t = A' s time, implying that t+2 = B's time.
Since A's rate = 65 mph, the total distance traveled by A in t hours = 65t.
Since B's rate = 50 mph, the total distance traveled by B in t+2 hours = 50(t+2).
Since B travels BACK AND FORTH, while A travels only in only ONE DIRECTION, B's total distance must be twice A's total distance:
50(t+2) = 2(65t)
50t + 100 = 130t
100 = 80t
t = 100/80 = 5/4 = 1.25.

The correct answer is C.
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
Top
Legendary Member
Posts: 2499
Joined: Sun Oct 29, 2017 2:04 pm
Followed by:6 members

by swerve » Fri Apr 06, 2018 11:54 am
Hi,

$$65t=d$$
$$50(t+2)=2d$$
$$130t=50t+100$$
$$t=5/4=1.25hours$$
Option C.

Regards!
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8086
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

by Scott@TargetTestPrep » Thu Jul 05, 2018 3:55 pm
BTGmoderatorLU wrote:Both car A and car B set out from their original locations at exactly the same time and on exactly the same route. Car A drives from Morse to Houston at an average speed of 65 miles per hour. Car B drives from Houston to Morse at 50 miles per hour, and then immediately returns to Houston at the same speed and on the same route. If car B arrives in Houston 2 hours after car A, how many hours did it take car A to make its trip?

A. 0.50
B. 1.00
C. 1.25
D. 1.33
E. 2.00
We can let the distance between Morse and Houston = d miles. So the time it takes car A to drive from Morse to Houston is d/65. Since car B arrives in Houston 2 hours after car A and it also drives double the distance, we can create the following equation:

2d/50 = d/65 + 2

Multiplying both sides by 650, we have:

26d = 10d + 1300

16d = 1300

d = 81.25

Therefore, it takes car A 81.25/65 = 1.25 hours to make the trip from Morse to Houston.

Alternate Solution:

Let the time car A takes to drive from Morse to Houston be t. Since car A drives at 65 mph, the distance between Morse and Houston, in terms of t, is 65t.

We are given that it takes t + 2 hours for car B to drive twice the distance between Morse and Houston; thus:

65t = [50(t + 2)]/2

130t = 50t + 100

80t = 100

t = 100/80 = 5/4 = 1.25 hours

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1