John drove on a highway at a constant speed of r miles per hour in 13:

Question

Math Revolution and GMAT Club Contest Starts!

QUESTION #12:

John drove on a highway at a constant speed of r miles per hour in 13:00. Then, 2 hours later, Tom drove on the same highway at a constant speed of 4r/3 miles per hour in 15:00. If both drivers maintained their speed, how many did John drive on a highway, in miles, when Tom caught up with John?

A. 3r
B. 5r
C. 8r
D. 9r
E. 10r

Check conditions below:

Show Spoiler

Math Revolution and GMAT Club Contest

The Contest Starts November 28th in Quant Forum

We are happy to announce a Math Revolution and GMAT Club Contest

For the following four (!) weekends we'll be publishing 4 FRESH math questions per weekend (2 on Saturday and 2 on Sunday).

To participate, you will have to reply with your best answer/solution to the new questions that will be posted on Saturday and Sunday at 9 AM Pacific.
Then a week later, the forum moderator will be selecting 2 winners who provided most correct answers to the questions, along with best solutions. Those winners will get 6-months access to GMAT Club Tests.

PLUS! Based on the answers and solutions for all the questions published during the project ONE user will be awarded with ONE Grand prize:

PS + DS course with 502 videos that is worth $299!

All announcements and winnings are final and no whining :-)

GMAT Club reserves the rights to modify the terms of this offer at any time.

NOTE: Test Prep Experts and Tutors are asked not to participate. We would like to have the members maximize their learning and problem solving process.

Thank you!

GMAT Club reserves the rights to modify the terms of this offer at any time. NOTE: Test Prep Experts and Tutors are asked not to participate. We would like to have the members maximize their learning and problem solving process. Thank you!

abhib3388 · Accepted Answer

Relative speed of tom with reference to john=(4r/3)-r=r/3
The distance john would have travelled in 2 hours=2r
Time taken by tom to catch up with john=2r/(r/3)=6 hours
When tom catches up with john,
total Distance travelled by john=total distance travelled by tom
2r+6r= 6*(4r/3)
 =8r
Answer C

pksam · Answer

John drove on a highway at a constant speed of r miles per hour in 13:00. Then, 2 hours later, Tom drove on the same highway at a constant speed of 4r/3 miles per hour in 15:00. If both drivers maintained their speed, how many did John drive on a highway, in miles, when Tom caught up with John?

A. 3r 
B. 5r 
C. 8r 
D. 9r 
E. 10r
Explanation:-
Suppose Tom drove for time t  speed  4r/3(given) And John for time t+2  speed  r ( given) 
Since both distance are equal hence t.4r/3=(t+2).r-->t=6
There fore John travelled 8r distance  ANS-C

HieuNguyenVN · Answer

When Tom started driving, the distance the John had already traveled is: 2r miles
Each hour the distance between Tom and John shortened by (4r/3-r) = r/3 miles
Then it will take Tom  \frac{2r}{(r/3)}=6  hours to catch up John, which means till Tom caught up with John, John had been driving for 8 hours => The distance John drove is 8r
Answer C.

mango aadmi · Answer

for 2 hrs, J travelled 2r miles.. now tom starts with 4r/3 speed.. suppose they meet after time T.. distance travelled by tom = 4rT/3

also John will travell rT miles in this time..
now.. 2r+rT = 4rT/3
2r=rT/3
T=6

Therefore John travels = 2r +6r = 8r miles
C

Lazure · Answer

The key thing to understand here is that when Tom catches up with John, they have covered the same distance.  What the question really asks for is this distance, which is expressed as  T * R  in the answer choices. So our goal is to express the distance covered by John and Tom with rate and time.

Distance covered by John :  
 2 * r (distance covered during the first 2 hours at r miles)
We define a new variable,  T  = the time it took John to travel the second portion of the trip. The distance he covers is  r * T .
Total distance covered by John:  2r + rT .

Distance covered by Tom : 
Tom travels at a speed of  \frac{4}{3}r .
The total travel time of Tom is equal to the time it takes John to travel the second part of his trip -->  T .
Total distance covered by Tom:  \frac{4}{3}rT

Since John and Tom have covered the same distance when they meet up, we can solve the following equation for T : 
 2r + rT = \frac{4}{3}rT 
 2r = \frac{1}{3}rT 
 T = 6 .
So it took Tom 6 hours to catch up with John.

And the distance covered is :
 \frac{4}{3}r * 6 = 8r

Answer C.

Bunuel · Answer

MATH REVOLUTION OFFICIAL SOLUTION: It is important to note that in speed problems, time passes at the same time. https://gmatclub.com/forum/download/file.php?id=28705 John traveled 2r miles during the first 2 hours and he traveled rt miles during the next t hours. In case of Tom, he traveled 4rt/3 miles during t hours. The distances they traveled are rt and 4rt/3, respectively,instead of rt1 and 4rt2/3,respectively because both traveled during the same time period. Then, 2r+rt=\frac{4rt}{3} → 2+t=\frac{4t}{3} → t=6. This means that Tom caught up with John after John traveled 6 hours. So we can solve 2r+6r=8r, and the correct answer is C . 2015-12-20_2149.png

giovannisumano · Answer

Math Revolution and GMAT Club Contest Starts!

QUESTION #12:

John drove on a highway at a constant speed of r miles per hour in 13:00. Then, 2 hours later, Tom drove on the same highway at a constant speed of 4r/3 miles per hour in 15:00. If both drivers maintained their speed, how many did John drive on a highway, in miles, when Tom caught up with John?

A. 3r 
B. 5r 
C. 8r 
D. 9r 
E. 10r

Let t be the time john drove before meeting with tom
distance drove by john = rt
distance drove by tom = 4/3r(t-2)

so rt=4/3r(t-2)
solving for t, t=8
therefore john drove 8r miles before meeting with tom

By the way, the redaction of this question is very poor

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

John drove on a highway at a constant speed of r miles per hour in 13:

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

John drove on a highway at a constant speed of r miles per hour in 13:

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards