The time it took car A to travel 400 miles was 2 hours less than the

Expert replies

Previous Topic Next Topic

BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pmFollowed by: 1 member

by BTGModeratorVI » Fri Jun 05, 2020 11:43 am

Timer

00:00

Answers

Stats

Difficulty—

The time it took car A to travel 400 miles was 2 hours less than the time it took car B to travel the same distance. If car A's average speed was 10 miles per hour greater than that of car B, what was car B's average speed in miles per hour?

A. 20
B. 30
C. 40
D. 50
E. 80

Answer: C
Source: GMAT paper tests

Like this post

Source: Beat The GMAT — Problem Solving | Fri Jun 05, 2020 11:43 am

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: The time it took car A to travel 400 miles was 2 hours less than the

by Brent@GMATPrepNow » Wed Jun 10, 2020 5:25 am

BTGModeratorVI wrote: ↑
Fri Jun 05, 2020 11:43 am
The time it took car A to travel 400 miles was 2 hours less than the time it took car B to travel the same distance. If car A's average speed was 10 miles per hour greater than that of car B, what was car B's average speed in miles per hour?

A. 20
B. 30
C. 40
D. 50
E. 80

Answer: C
Source: GMAT paper tests

Car A's average speed was 10 miles per hour greater than that of car B
Let x = Car B's average speed
So, x + 10 = Car A's average speed

The time it took car A to travel 400 miles was 2 hours less than the time it took car B to travel the same distance
In other words: (car A's travel time) = (car B's travel time) - 2

time = distance/speed
So, we get: 400/(x + 10)) = 400/x - 2

NOTE: At this point, we can either test the five answer choices to see which one satisfies the above equation, or we can solve the equation algebraically.
Although testing the answer choices is probably faster, let's solve the equation algebraically
Multiply both sides of the equation by (x + 10) to get: 400 = 400(x + 10)/x - (x + 10)(2)
Multiply both sides of the equation by x to get: 400x = 400(x + 10) - (x)(x + 10)(2)
Expand: 400x = 400x + 4000 - 2x² - 20x
Subtract 400x from both sides to get: 0 = 4000 - 2x² - 20x
Multiply both sides by -1 to get: 0 = -4000 + 2x² + 20x
Rewrite as follows: 2x² + 20x - 4000 = 0
Divide both sides by 2 to get: x² + 10x - 2000 = 0
Factor: (x + 50)(x - 40) = 0
So, EITHER x = -50 OR x = 40
Since the speed can't be negative, it must be the case that x = 40

Answer: C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8152; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: The time it took car A to travel 400 miles was 2 hours less than the

by Scott@TargetTestPrep » Fri Jun 12, 2020 1:43 pm

BTGModeratorVI wrote: ↑
Fri Jun 05, 2020 11:43 am
The time it took car A to travel 400 miles was 2 hours less than the time it took car B to travel the same distance. If car A's average speed was 10 miles per hour greater than that of car B, what was car B's average speed in miles per hour?

A. 20
B. 30
C. 40
D. 50
E. 80

Answer: C

Solution:

We are given that cars A and B both traveled 400 miles and that car A’s average speed was 10 mph greater than that of car B. We can let the rate of car B = r and the rate of car A = r + 10.

Since both cars traveled 400 miles and time = distance/rate, the time of car A is 400/(r+10).

We are also given that it took car A 2 hours less than it took car B to travel the 400 miles. We can set up the following equation:

400/(r+10) + 2 = 400/r

Multiplying the entire equation by r(r+10), we have:

400r + 2(r)(r+10) = 400(r+10)

400r + 2r^2 + 20r = 400r + 4000

2r^2 + 20r - 4000 = 0

r^2 + 10r - 2000 = 0

(r + 50)(r - 40) = 0

r = -50 or r = 40

Since r must be positive, then r = 40.

Answer: C

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

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 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