Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 13 Sep 2016
Posts: 117

A canoeist spent two days on a large lake. On the second day, the cano [#permalink]
Show Tags
17 Oct 2016, 22:46
8
This post was BOOKMARKED
Question Stats:
73% (02:02) correct 27% (02:35) wrong based on 190 sessions
HideShow timer Statistics
A canoeist spent two days on a large lake. On the second day, the canoeist rowed 2 hours longer and at an average speed 2 miles per hour faster than he rowed on the first day. If the canoeist traveled a total of 50 miles and spent a total of 12 hours rowing on his trip, what was his average speed on the first day? a) 2mph b) 3mph c) 4mph d) 5mph e) 6mph
Official Answer and Stats are available only to registered users. Register/ Login.



Intern
Joined: 12 Jul 2012
Posts: 2

Re: A canoeist spent two days on a large lake. On the second day, the cano [#permalink]
Show Tags
17 Oct 2016, 23:15
1
This post received KUDOS
1
This post was BOOKMARKED
Let time taken be t1 and t2 for day 1 and 2 respectively. So t1+t2=12 and t2=t1+2. Substituting we get t1 = 5 and t2=7. Since total distance travelled is 50 we can say 50=5X + 7 (X+2) where X is avg speed of day 1. Solving we get X=3 and hnc the answer.
We can also solve just by looKing at numbers the, avg speed is 50/12 which is 4.1... so the average of 2 days must be around 4 and also satisfy the statement that average speed of day 2 is 2 mph more. 3 and 5 is the right combination. Plz correct me if am wrong.
Posted from my mobile device



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3441
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Re: A canoeist spent two days on a large lake. On the second day, the cano [#permalink]
Show Tags
18 Oct 2016, 00:37
2
This post received KUDOS
alanforde800Maximus wrote: A canoeist spent two days on a large lake. On the second day, the canoeist rowed 2 hours longer and at an average speed 2 miles per hour faster than he rowed on the first day. If the canoeist traveled a total of 50 miles and spent a total of 12 hours rowing on his trip, what was his average speed on the first day?
a) 2mph b) 3mph c) 4mph d) 5mph e) 6mph
Please assist with above problem. Form a table it will be a cake walk  Attachment:
Screenshot.jpg [ 10.75 KiB  Viewed 1862 times ]
Here, 2t + 2 = 12 Or, 2t = 10 Or, t = 5 Further  5*s + ( 5 + 2 ) (s + 2 ) = 50 or, 5s + 7s + 14 = 50 Or, 12s = 36 So, S = 3 Hence answer will be (B) 3
_________________
Thanks and Regards
Abhishek....
PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS
How to use Search Function in GMAT Club  Rules for Posting in QA forum  Writing Mathematical Formulas Rules for Posting in VA forum  Request Expert's Reply ( VA Forum Only )



Manager
Joined: 29 Aug 2008
Posts: 110

Re: A canoeist spent two days on a large lake. On the second day, the cano [#permalink]
Show Tags
19 Oct 2016, 02:05
2
This post received KUDOS
t1 + t2 = 12 and t2  t1 = 2 solving for t1 and t2, t1 =5 t2 = 7
Total Distance = 50 = S*5 + (S+2)7 Solving for S, S = 3
HTH



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2597
Location: United States (CA)

Re: A canoeist spent two days on a large lake. On the second day, the cano [#permalink]
Show Tags
05 Dec 2017, 18:32
alanforde800Maximus wrote: A canoeist spent two days on a large lake. On the second day, the canoeist rowed 2 hours longer and at an average speed 2 miles per hour faster than he rowed on the first day. If the canoeist traveled a total of 50 miles and spent a total of 12 hours rowing on his trip, what was his average speed on the first day?
a) 2mph b) 3mph c) 4mph d) 5mph e) 6mph We are given that on a second day the canoeist rowed 2 hours longer and at an average speed 2 miles per hour faster than he rowed on the first day. If we let the number of hours the canoeist rowed on the first day = t, then the number of hours that he canoeist rowed on the second day = t + 2. Also, if we let the rate of the canoeist on the first day = r, then the rate of the canoeist on the second day is r + 2. Since we are given that the total time spent rowing was 12 hours, we can determine a value for t. t + t + 2 = 12 2t = 10 t = 5 Thus, 5 hours was spent rowing on day one, and 7 hours on day 2. We are also given that the canoeist traveled a total of 50 miles. Since distance = rate x time, we can represent the distance traveled on day one as 5r and the distance traveled on day two as 7(r+2) = 7r + 14. Thus: 5r + 7r + 14 = 50 12r = 36 r = 3 Answer: B
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11647
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: A canoeist spent two days on a large lake. On the second day, the cano [#permalink]
Show Tags
23 Jan 2018, 15:22
Hi All, Certain versions of this prompt will require lots of 'math steps' to get to the solution, but this specific prompt can be solved with a bit of logic and just a little math. To start, we're told that the TOTAL trip was 50 miles and took 12 hours. That's an average of 50/12 = 4 1/6 miles/hour. We're told that the two speeds differed by 2 miles/hour, and we spent just 2 extra hours at the faster speed. Thus, the slower speed was measurably below 4 1/6 mph and the upper speed was measurably above 4 1/6 mph. Remember  the speeds DIFFER by 2mph. We're asked for the speed on the first day (re: the slower speed). Looking at the answer choices, we can quickly compare what each answer implies to what the math dictates must happen... Answer A: slow speed = 2mph, fast speed = 4mph. Does not make sense (the faster speed has to be GREATER than 4mph). Answer B: slow speed = 3mph, fast speed = 5mph. This matches the logic really nicely. Answer C: slow speed = 4mph, fast speed = 6mph. Here, the slow speed is just barely below the average speed, which doesn't make sense. The remaining two answers will just get further and further away from the average, so we don't have to think much about them. Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Retired Moderator
Status: The best is yet to come.....
Joined: 10 Mar 2013
Posts: 516

Re: A canoeist spent two days on a large lake. On the second day, the cano [#permalink]
Show Tags
06 Feb 2018, 18:52
EMPOWERgmatRichC wrote: Answer C: slow speed = 4mph, fast speed = 6mph. Here, the slow speed is just barely below the average speed, which doesn't make sense. Rich I don't get why answer C doesn't make sense. Would you please see my following reasoning? If the canoeist covers 44 miles at slower speed 4mph and remaining 6 miles at faster speed 6mph, then the time taken would be 11 hours and 1 hour respectively. Total time would be 12 hours. Attachment:
Canoeist spent.JPG [ 18.04 KiB  Viewed 515 times ]
Am I wrong?
_________________
Hasan Mahmud



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11647
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: A canoeist spent two days on a large lake. On the second day, the cano [#permalink]
Show Tags
07 Feb 2018, 12:02
Hi Mahmud6, You're overlooking an important piece of information in the prompt: the canoeist spent just 2 hours longer rowing at the FASTER speed (meaning that he spent 5 hours at the slower speed and 7 hours at the faster speed). Your example has the canoeist spending TEN hours longer at the SLOWER speed. In mathterms, this is essentially a Weighted Average  however, the amount of time spent at each speed isn't that different from the other  so the average won't be weighted too heavily in either direction (meaning that the average speed is NOT 'really close' to either speed). We calculated that the average speed was 4 1/6 mph, so we can think about how weighted averages "work"... One hour at 3 mph and one hour at 5 mph = (8 miles)/(2 hours) = 4 mph One hour at 3 mph and two hours at 5 mph = (13 miles)/(3 hours) = 4 1/3 mph Notice in the second example that we spent DOUBLE the amount of time at the faster speed and ended up with an average that was GREATER than 4 1/6 mph. That ratio is 'too much' relative to what we're told in the prompt  and it led to an average speed that was too high. 3mph and 5mph are perfect speeds for this situation; these examples just don't use the proper ratio. From the answers, we know that the slower speed is an INTEGER (and from the prompt, we know that the faster speed would also be an INTEGER). Thus, the two speeds would have to be 3mph and 5 mph. GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Retired Moderator
Status: The best is yet to come.....
Joined: 10 Mar 2013
Posts: 516

Re: A canoeist spent two days on a large lake. On the second day, the cano [#permalink]
Show Tags
07 Feb 2018, 22:22
EMPOWERgmatRichC wrote: Hi Mahmud6,
You're overlooking an important piece of information in the prompt: the canoeist spent just 2 hours longer rowing at the FASTER speed (meaning that he spent 5 hours at the slower speed and 7 hours at the faster speed). Your example has the canoeist spending TEN hours longer at the SLOWER speed.
In mathterms, this is essentially a Weighted Average  however, the amount of time spent at each speed isn't that different from the other  so the average won't be weighted too heavily in either direction (meaning that the average speed is NOT 'really close' to either speed). We calculated that the average speed was 4 1/6 mph, so we can think about how weighted averages "work"...
One hour at 3 mph and one hour at 5 mph = (8 miles)/(2 hours) = 4 mph One hour at 3 mph and two hours at 5 mph = (13 miles)/(3 hours) = 4 1/3 mph
Notice in the second example that we spent DOUBLE the amount of time at the faster speed and ended up with an average that was GREATER than 4 1/6 mph. That ratio is 'too much' relative to what we're told in the prompt  and it led to an average speed that was too high. 3mph and 5mph are perfect speeds for this situation; these examples just don't use the proper ratio.
From the answers, we know that the slower speed is an INTEGER (and from the prompt, we know that the faster speed would also be an INTEGER). Thus, the two speeds would have to be 3mph and 5 mph.
GMAT assassins aren't born, they're made, Rich Thank you Rich. Got it.
_________________
Hasan Mahmud




Re: A canoeist spent two days on a large lake. On the second day, the cano
[#permalink]
07 Feb 2018, 22:22






