Car X left Town T (RATE PROBLEM, Need Help)

Expert replies

mkbigmoz: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Sun Feb 08, 2009 4:53 pmFollowed by: 1 member; Thanked: 3 times

by mkbigmoz » Tue Apr 07, 2009 8:27 am

Im completely confused with the answer...I know I must be overlooking something.

Car X left Town T traveling at an average speed of 40 miles per hour. Car Y left Town T 18 minutes after car X left Town T, and car Y traveled at an average speed of 54 miles per hour. When car Y had traveled for z minutes, car Y had traveled 23 miles more that car X had from the time that car X left Town T. What is the value of z ?

A 81
B 90
C 105
D 125
E 150

[spoiler]
E 150

If the answer is E, wouldn't car Y have traveled 135 miles further than car X?[/spoiler]

Like this post

Source: Beat The GMAT — Problem Solving | Tue Apr 07, 2009 8:27 am

moutar: Senior | Next Rank: 100 Posts; Posts: 92; Joined: Wed Mar 25, 2009 12:13 pm; Thanked: 10 times

by moutar » Tue Apr 07, 2009 8:47 am

distance = speed x time

Car X travels at 40 mph for (z+18)mins = (z+18)/60 hours
Distance = 40(z+18)/60

Car Y travels at 54mph for z mins = z/60 hours
Distance = 54z/60

Car Y travels 23 miles more than Car X so:

(40(z+18)/60) + 23= 54z/60

40(z+18) + 23*60 = 54z (multiply through by 60)

40z + 720 + 1380 = 54z (multiplying out)

14z = 2100 (collecting like terms)

z = 150 (E)

Like this post

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Fri Dec 28, 2018 9:19 am

mkbigmoz wrote:Car X left Town T traveling at an average speed of 40 miles per hour. Car Y left Town T 18 minutes after car X left Town T, and car Y traveled at an average speed of 54 miles per hour. When car Y had traveled for z minutes, car Y had traveled 23 miles more that car X had from the time that car X left Town T. What is the value of z ?
A 81
B 90
C 105
D 125
E 150

IMPORTANT: Let's use HOURS throughout our solution, and then convert hours to minutes at the end.

When car Y had traveled for z HOURS, car Y had traveled 23 miles more that car X had from the time that car X left Town T.
z = car Y's travel time in HOURS
So, z + 3/10 = car X's travel time in HOURS
[18 minutes = 3/10 HOURS, and car X traveled for 18 minutes before car Y started moving]

We can write: (car Y's distance traveled) - (car X's distance traveled) = 23 miles

distance = (speed)(time)
So, we get: (54)(z) - (40)(z + 3/10) = 23 miles
Expand to get: 54z - 40z - 12 = 23
Simplify: 14z - 12 = 23
So: 14z = 35
Solve: z = 35/14 = 5/2 = 2.5 HOURS
= 150 MINUTES

Answer: E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

jaetpu: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Tue Nov 14, 2017 2:51 pm

by jaetpu » Thu Jan 03, 2019 10:57 pm

mkbigmoz wrote:Im completely confused with the answer...I know I must be overlooking something.

Car X left Town T traveling at an average speed of 40 miles per hour. Car Y left Town T 18 minutes after car X left Town T, and car Y traveled at an average speed of 54 miles per hour. When car Y had traveled for z minutes, car Y had traveled 23 miles more that car X had from the time that car X left Town T. What is the value of z ?

A 81
B 90
C 105
D 125
E 150

[spoiler]
E 150

If the answer is E, wouldn't car Y have traveled 135 miles further than car X?[/spoiler]

Let's make this into a simple D=RT problem. Since car X had been traveling for 18 minutes before car Y left, car X must be (18/60)hr*40mph = 12 miles ahead. Later, we learn that car Y had traveled 23 miles more than X. To sum it up, Car Y needs to catch up 35 miles to be 23 ahead of X.

Car Y travels 14mph faster than Car X. So 35=14mph * t. 35/14 = 2.5 hrs = t. 2.5 hrs in minutes is 150.

Like this post

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8211; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Fri Feb 01, 2019 5:42 pm

mkbigmoz wrote:Im completely confused with the answer...I know I must be overlooking something.

Car X left Town T traveling at an average speed of 40 miles per hour. Car Y left Town T 18 minutes after car X left Town T, and car Y traveled at an average speed of 54 miles per hour. When car Y had traveled for z minutes, car Y had traveled 23 miles more that car X had from the time that car X left Town T. What is the value of z ?

A 81
B 90
C 105
D 125
E 150

We are given that Car X traveled at a rate of 40 mph and Car Y at a rate of 54 mph.

Since car Y left 18 minutes after car X, car Y traveled for z minutes, or z/60 hours, and car X for (z + 18) minutes or (z + 18)/60 hours; thus:

40[(z + 18)/60] + 23 = 54(z/60)

Multiplying by 60, we have:

40(z + 18) + 1380 = 54z

40z + 720 + 1380 = 54z

2100 = 14z

z = 2100/14 = 150

Answer: E

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

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

563 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (563 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review