During a trip on an expressway, Don drove a total of...

Expert replies

swerve: Legendary Member; Posts: 2579; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Fri Dec 22, 2017 1:43 pm

During a trip on an expressway, Dron drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for x-mile trip was what percent greater than it would have been if he has traveled at a constant rate of 60 miles per hour for the entire trip?

A. 8.5%
B. 50%
C. x/12%
D. 60/x%
E. 500/x%

The OA is E.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

Like this post

Source: Beat The GMAT — Problem Solving | Fri Dec 22, 2017 1:43 pm

regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

by regor60 » Wed Dec 27, 2017 11:08 am

swerve wrote:During a trip on an expressway, Dron drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for x-mile trip was what percent greater than it would have been if he has traveled at a constant rate of 60 miles per hour for the entire trip?

A. 8.5%
B. 50%
C. x/12%
D. 60/x%
E. 500/x%

The OA is E.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

Use Distance = Rate x Time. Call the total distance X per the problem.

Call the total time for the slower overall trip T. Call the time for the trip at 60 mph T1.

Transcribing the slower trip: X [distance] = 5 [30 mph distance] + 60 mph*(T-1/6) [time spent at 60mph is total time minus time spent at 30mph]

So X = 5+ 60T-10 = 60T-5

Now rearrange to find T since the question wants to know something about the times: T = (X+5)/60

Transcribe the faster trip: X [same distance] = 60 mph*T1 > Solve for T1 = X/60

The difference between these times is T1-T = (X+5)/60 - X/60 = 5/60

The question asks for the percentage of the faster time this difference is. First find the decimal equivalent:

(5/60)/T1 = (5/60)/(X/60) = (5/60)*(60/X) = 5/X

5/X is the decimal answer. To put in terms of percent, multiply by 100 = [spoiler]500/X, E[/spoiler]

Like this post

GMATWisdom: Master | Next Rank: 500 Posts; Posts: 100; Joined: Wed Nov 29, 2017 4:38 pm; Thanked: 14 times

by GMATWisdom » Wed Dec 27, 2017 4:54 pm

swerve wrote:During a trip on an expressway, Dron drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for x-mile trip was what percent greater than it would have been if he has traveled at a constant rate of 60 miles per hour for the entire trip?

A. 8.5%
B. 50%
C. x/12%
D. 60/x%
E. 500/x%

The OA is E.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

In the first case he has traveled first 5 miles at a speed of 30mph and in the second case
he travells same 5 miles at the speed of 60 miles per hour
therefore the the difference in travel time would be 5/30 - 5/60 = 5/60 = 1/12 hours.
travel time for distance X miles at the rate of 60 miles per hour = X/ 60 hours
Hence percentage increase in time = (1/12)*100/(X/60)= 500/X
Hence option E

Like this post

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8207; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Wed Sep 04, 2019 5:20 pm

swerve wrote:During a trip on an expressway, Dron drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for x-mile trip was what percent greater than it would have been if he has traveled at a constant rate of 60 miles per hour for the entire trip?

A. 8.5%
B. 50%
C. x/12%
D. 60/x%
E. 500/x%

The OA is E.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

We are given that Don drove a total of x miles, his average speed on a 5-mile section of the expressway was 30 mph, and his average speed for the remainder of the trip, or x - 5 miles, was 60 mph.

Since time = distance/rate, the time for the first 5-mile section was 5/30 = 1/6 of an hour, and the time for the remainder of the trip was (x-5)/60 hours.

Thus, the total time was 1/6 + (x-5)/60 = 10/60 + (x-5)/60 = (x + 5)/60 hours.

Had he traveled at a constant rate of 60 miles per hour for the entire trip, then his time would have been x/60 hours.

We need to determine the percent by which (x + 5)/60 is greater than x/60. We use the percent change formula: (New - Old)/Old * 100%.

[(x + 5)/60 - x/60]/(x/60) * 100%

(5/60)/(x/60) * 100%

5/x * 100%

500/x%

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

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

Re: During a trip on an expressway, Don drove a total of...

by Brent@GMATPrepNow » Tue Nov 16, 2021 9:39 am

swerve wrote: ↑
Fri Dec 22, 2017 1:43 pm
During a trip on an expressway, Dron drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for x-mile trip was what percent greater than it would have been if he has traveled at a constant rate of 60 miles per hour for the entire trip?

A. 8.5%
B. 50%
C. x/12%
D. 60/x%
E. 500/x%

The OA is E.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

Don drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour.
Total time = (time spent driving 30 mph) + (time spent driving 60 mph)
time = distance/speed
So, total driving time = 5/30 + (x - 5)/60
= 10/60 + (x - 5)/60
= (10 + x - 5)/60
= (x + 5)/60

Hypothetically speaking, Don could have driven the entire x miles at a speed of 60 mph
time = distance/speed
Total driving time = x/60

His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip?
In other word: (x + 5)/60 is what percent greater than x/60?

Percentage = 100[(x + 5)/60 - x/60]/(x/60)
= 100[5/60]/(x/60)
= 100(5/60)(60/x)
= 500/x

Answer: E

Brent Hanneson - Creator of GMATPrepNow.com

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