Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 22 Mar 2010
Posts: 54

A car travels from Mayville to Rome at an average speed of 3 [#permalink]
Show Tags
Updated on: 27 Jun 2013, 01:26
4
This post was BOOKMARKED
Question Stats:
76% (01:09) correct 24% (01:02) wrong based on 317 sessions
HideShow timer Statistics
A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round trip? ○ 32.0 ○ 33.0 ○ 34.3 ○ 35.5 ○ 36.5
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by EnterMatrix on 18 Jul 2010, 10:53.
Last edited by Bunuel on 27 Jun 2013, 01:26, edited 1 time in total.
Edited the OA.



Math Expert
Joined: 02 Sep 2009
Posts: 44599

Re: Speed Distance [#permalink]
Show Tags
18 Jul 2010, 14:34
4
This post received KUDOS
Expert's post
2
This post was BOOKMARKED
EnterMatrix wrote: A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round trip? ○ 32.0 ○ 33.0 ○ 34.3 ○ 35.5 ○ 36.5 Choose some smart number for the distance from Mayville to Rome: let the distance be 120 miles (120 is LCM of 30 and 40 and this will make further calculations easier). \(Average \ speed=\frac{total \ distance}{total \ time}\) > so the nominator, total distance would be \(2*120=240\); Total time equals time from Mayville to Rome plus time from Rome to Mayville > \(\frac{120}{30}+\frac{120}{40}=7\); \(Average \ speed=\frac{total \ distance}{total \ time}=\frac{240}{7}\approx{34.3}\). Answer: C.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 20 Jul 2010
Posts: 161

Re: Speed Distance [#permalink]
Show Tags
20 Jul 2010, 06:57
3
This post received KUDOS
IMO CEnterMatrix wrote: A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round trip? ○ 32.0 ○ 33.0 ○ 34.3 ○ 35.5 ○ 36.5 Solution: Average speed for the entire trip = 2uv/(u+v), where u = speed of going v = speed of returningThus, average speed = 2*40*30/(70) = 34.3 mi/h Hence, C
_________________
Gotta hit the 700 score this time... 3rd time lucky ! Give me some kudos... Like you, even I need them badly



Intern
Joined: 26 Mar 2010
Posts: 13

Re: Speed Distance [#permalink]
Show Tags
20 Jul 2010, 10:20
1
This post received KUDOS
EnterMatrix wrote: A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round trip? ○ 32.0 ○ 33.0 ○ 34.3 ○ 35.5 ○ 36.5 It is pretty involuntary to come up with 35 miles per hour as the average speed in this case. But, that is wrong. Since, the car has taken more time to travel at 30 mph and less time to travel at 40 mph, the avg speed of the car would be somewhere between 30 and 35(mean) and closer to 35. If I had no time on my hands and had to make a calculated guess, I would have chosen C. The correct way to find the avg speed is to calculate the total distance and the total time and divide the total distance by total time. Let the one way distance in this case be D. So the total distance is 2D(travelled over the same route twice) Total Time = Time taken to travel distance D at 30 mph + time taken to travel distance D at 40 mph = \((D/30) + (D/40)\) = \(7D/120\) Thus avg speed = Total distance/total time = \((2D)/(7D/120)\) = 34.285 Hope it helps, meshtrap



Manager
Joined: 06 Jun 2014
Posts: 92
Location: United States
Concentration: Finance, General Management
GPA: 3.47

A car travels from Mayville to Rome at an average speed of 3 [#permalink]
Show Tags
27 Apr 2015, 12:47
We can pick any number for distance that is divisible by both 30 and 40. Since we have rate and distance, by plugging in the rate formula (r=d/t) we can solve for the average rate/speed City``` Rate Time Distance MR.... 30 4  120 RM ... 40  3  120 Total 34.28  7  240
34.28 ~ 34.3
_________________
1) Kaplanprep 450 Q27 V21 2) Manhattan 530 Q35 V28 3) GmatPrep 450 Q33, V19 4) Veritas 460 Q31, V23 5) Veritas 440 Q 30, V21 6) Veritas 500 Q34, V 25 7) Gmat 420 Q27, V23 8) Veritas 520 Q36, V26 2/2 9) Veritas 540 Q37, V28 4/19 10)Manhattan 560 Q40, V28 4/28



Director
Joined: 12 Nov 2016
Posts: 776

Re: A car travels from Mayville to Rome at an average speed of 3 [#permalink]
Show Tags
13 Aug 2017, 13:22
EnterMatrix wrote: A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round trip?
○ 32.0 ○ 33.0 ○ 34.3 ○ 35.5 ○ 36.5 This is just an approximation and round trip problem we simply pick a value which is usually the LCM Total Distance= Avgspeed * Total Time 120/30= 4 120/40= 3 240= average speed * 7 240/7= 34.3



SVP
Joined: 12 Sep 2015
Posts: 2298
Location: Canada

Re: A car travels from Mayville to Rome at an average speed of 3 [#permalink]
Show Tags
03 Apr 2018, 10:15
EnterMatrix wrote: A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round trip?
A) 32.0 B) 33.0 C) 34.3 D) 35.5 E) 36.5 We can solve this one quickly if we assign a "nice" distance between Mayville and Rome ("nice" means a distance that works well with 30 miles per hour AND 40 miles per hour) So, let's say the distance between Mayville and Rome = 120 milesTime = distance/speedSo, time from Mayville and Rome (at 30 mph) = 120/30 = 4 hours Time from Rome to Mayville (at 40 mph) = 120/40 = 3 hours Average speed = (total distance traveled)/(total time) = ( 120 + 120)/( 4 + 3) = 240/7 = 34.something (if we use long division here, we'll stop once we get to the ones digit) Answer: C Cheers. Brent
_________________
Brent Hanneson – Founder of gmatprepnow.com



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2273

Re: A car travels from Mayville to Rome at an average speed of 3 [#permalink]
Show Tags
05 Apr 2018, 17:00
EnterMatrix wrote: A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round trip?
○ 32.0 ○ 33.0 ○ 34.3 ○ 35.5 ○ 36.5 We can use the average rate formula: average = total distance/total time, and let the distance each way = 120 miles. (Note that we could use any number for the distance, but we have chosen the convenient number 120 because it is evenly divisible by both 30 and 40, making the arithmetic easier.) average = 240/(120/30 + 120/40) average = 240/(4 + 3) = 240/7 = 34.3 Answer: C
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Director
Status: It's near  I can see.
Joined: 13 Apr 2013
Posts: 718
Location: India
Concentration: International Business, Operations
GPA: 3.01
WE: Engineering (Consulting)

Re: A car travels from Mayville to Rome at an average speed of 3 [#permalink]
Show Tags
15 Apr 2018, 00:52
EnterMatrix wrote: A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round trip?
○ 32.0 ○ 33.0 ○ 34.3 ○ 35.5 ○ 36.5 Total distance = D + D = 2D Total time = D/30 +D/40 Avg. Speed = Total distance / Total time Avg. Speed =\(\frac{(2D)}{(D/30 + D/40)}\) Avg. Speed = \(\frac{240D}{70D}\) Avg. Speed = 34.2 approx Hence (C)
_________________
"Success is not as glamorous as people tell you. It's a lot of hours spent in the darkness."




Re: A car travels from Mayville to Rome at an average speed of 3
[#permalink]
15 Apr 2018, 00:52






