Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Apr 1612:00 PM EDT
-11:59 PM EDT
You’re first to know: Save $200 on GMAT prep starting tomorrow, 4/13. Get 6 official practice tests and study with real questions. Be ready to save!
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
08 Jan 2025, 03:06
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
100% (01:58) correct
0%
(00:00)
wrong
based on 3
sessions
History
Date
Time
Result
Not Attempted Yet
Ross is biking at a constant rate of \(x\) miles per hour along a straight route when he is overtaken by Rachel, who is also traveling along the same route at a constant speed 4 times faster than his. After driving for \(t\) minutes, Rachel takes a break and stops to wait for Ross to catch up. If she had to wait 45 minutes for Ross to catch up, what is the value of \(t\)?
A. 10
B. 12
C. 15
D. 20
E. 45
A. 10
B. 12
C. 15
D. 20
E. 45
08 Jan 2025, 03:06
Kudos
Bookmarks
Official Solution:
Ross is biking at a constant rate of \(x\) miles per hour along a straight route when he is overtaken by Rachel, who is also traveling along the same route at a constant speed 4 times faster than his. After driving for \(t\) minutes, Rachel takes a break and stops to wait for Ross to catch up. If she had to wait 45 minutes for Ross to catch up, what is the value of \(t\)?
A. 10
B. 12
C. 15
D. 20
E. 45
Ross travels at \(x\) miles per hour, and Rachel travels at \(4x\) miles per hour.
The relative speed between them is \(4x - x = 3x\) miles per hour.
In \(t\) minutes (or \(\frac{t}{60}\) hours), the distance between Ross and Rachel becomes \((\frac{t}{60}) * 3x = \frac{tx}{20}\) miles.
For Ross to catch up, he needs \(\frac{(\frac{tx}{20})}{x} = \frac{t}{20}\) hours. Since this time equals \(\frac{3}{4}\) hours (45 minutes), we have:
\(\frac{t}{20} = \frac{3}{4}\), which simplifies to \(t = 15\) minutes.
Alternatively, we can think of it this way: In 45 minutes, Ross covered the distance at his speed of \(x\) miles per hour. This distance originated when Rachel was driving at the relative speed of \(3x\) miles per hour. Therefore, Rachel must have been driving for a third of the time it took Ross to catch up, or 15 minutes.
Answer: C
Ross is biking at a constant rate of \(x\) miles per hour along a straight route when he is overtaken by Rachel, who is also traveling along the same route at a constant speed 4 times faster than his. After driving for \(t\) minutes, Rachel takes a break and stops to wait for Ross to catch up. If she had to wait 45 minutes for Ross to catch up, what is the value of \(t\)?
A. 10
B. 12
C. 15
D. 20
E. 45
Ross travels at \(x\) miles per hour, and Rachel travels at \(4x\) miles per hour.
The relative speed between them is \(4x - x = 3x\) miles per hour.
In \(t\) minutes (or \(\frac{t}{60}\) hours), the distance between Ross and Rachel becomes \((\frac{t}{60}) * 3x = \frac{tx}{20}\) miles.
For Ross to catch up, he needs \(\frac{(\frac{tx}{20})}{x} = \frac{t}{20}\) hours. Since this time equals \(\frac{3}{4}\) hours (45 minutes), we have:
\(\frac{t}{20} = \frac{3}{4}\), which simplifies to \(t = 15\) minutes.
Alternatively, we can think of it this way: In 45 minutes, Ross covered the distance at his speed of \(x\) miles per hour. This distance originated when Rachel was driving at the relative speed of \(3x\) miles per hour. Therefore, Rachel must have been driving for a third of the time it took Ross to catch up, or 15 minutes.
Answer: C
19 Mar 2025, 04:44
Kudos
Bookmarks
How about this solution,
For Ross, Constant Speed = x
For Rachel Constant, speed = 4x
After t minutes, Rachel waited 45 minutes for Ross to catch up. So, Practically, Ross needs to cover same distance as rachel.
4xt = x(t+45)
=>4xt - xt = 45x
=> 3xt = 45x
=> t = 15 minute
Is this one correct approach?
For Ross, Constant Speed = x
For Rachel Constant, speed = 4x
After t minutes, Rachel waited 45 minutes for Ross to catch up. So, Practically, Ross needs to cover same distance as rachel.
4xt = x(t+45)
=>4xt - xt = 45x
=> 3xt = 45x
=> t = 15 minute
Is this one correct approach?
