Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 04 Mar 2012
Posts: 36

Two boats are heading towards each other at constant speeds
[#permalink]
Show Tags
01 May 2012, 20:29
Question Stats:
76% (02:23) correct 24% (02:52) wrong based on 739 sessions
HideShow timer Statistics
Two boats are heading towards each other at constant speeds of 5 miles/hr and 20 miles/hr respectively. They begin at a distance 20 miles from each other. How far are they (in miles) one minute before they collide ? A. 1/12 B. 5/12 C. 1/6 D. 1/3 E. 1/5
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 65785

Re: Two boats are heading towards each other at constant speeds
[#permalink]
Show Tags
01 May 2012, 21:52
gmihir wrote: Two boats are heading towards each other at constant speeds of 5 miles/hr and 20 miles/hr respectively. They begin at a distance 20 miles from each other. How far are they (in miles) one minute before they collide ?
A. 1/12 B. 5/12 C. 1/6 D. 1/3 E. 1/5 The question asks: how far apart will they be 1 minute=1/60 hours before they collide? Since the combined rate of the boats is 5+20=25 mph then 1/60 hours before they collide they'll be rate*time=distance > 25*1/60=5/12 miles apart. Answer: B. Similar question to practice: 12easypiecesornot126366.html#p1033924Hope it helps.
_________________




Intern
Joined: 04 Mar 2012
Posts: 36

Re: Two boats are heading towards each other at constant speeds
[#permalink]
Show Tags
02 May 2012, 21:34
Thanks Bunnel for the great link  awesome questions!!
For this one (two boats heading towards each other)  i calculated the time they would collide with each other (48th min) and then "tried" calculating from there on, taking eons to solve  how can the problem be solved with this apporach ? is 25*1/60 the only way to solve such problems ?



Math Expert
Joined: 02 Sep 2009
Posts: 65785

Re: Two boats are heading towards each other at constant speeds
[#permalink]
Show Tags
03 May 2012, 11:23
gmihir wrote: Thanks Bunnel for the great link  awesome questions!!
For this one (two boats heading towards each other)  i calculated the time they would collide with each other (48th min) and then "tried" calculating from there on, taking eons to solve  how can the problem be solved with this apporach ? is 25*1/60 the only way to solve such problems ? It's not the only way but for sure the shortest way to solve this problem.
_________________



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10784
Location: Pune, India

Re: Two boats are heading towards each other at constant speeds
[#permalink]
Show Tags
04 May 2012, 19:44
gmihir wrote: Thanks Bunnel for the great link  awesome questions!!
For this one (two boats heading towards each other)  i calculated the time they would collide with each other (48th min) and then "tried" calculating from there on, taking eons to solve  how can the problem be solved with this apporach ? is 25*1/60 the only way to solve such problems ? Bunuel has already given you a great and most direct approach for this question. But if you did go the round about way, you could have solved it in this way: Since their combined speed is 20 + 5 = 25 miles/hr, they cover 20 miles in \(\frac{20}{25}\) hrs i.e. \(\frac{20}{25} * 60\) mins = 48 mins Now, in 48 mins, they cover 20 miles. So in 1 min, they must have covered 20/48 = 5/12 miles
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Senior Manager
Joined: 24 Aug 2009
Posts: 427
Schools: Harvard, Columbia, Stern, Booth, LSB,

Re: Two boats are heading towards each other at constant speeds
[#permalink]
Show Tags
25 Aug 2012, 10:53
Hi Bunuel, Your explanation is always the best. I have a slightly different Logic to solve this question. Hope you will like the logic The question asks: How much distance will both travel in 1 minute? Since the combined rate of the boats is 5+20=25 mph = 25/60 mile/min = 5/12 mile/min Hence Answer: B.



Senior Manager
Joined: 13 May 2013
Posts: 389

Re: Two boats are heading towards each other at constant speeds
[#permalink]
Show Tags
06 Nov 2013, 18:21
Two boats are heading towards each other at constant speeds of 5 miles/hr and 20 miles/hr respectively. They begin at a distance 20 miles from each other. How far are they (in miles) one minute before they collide?
I probably did this a bit backwards but here is how I figured it out...
The boats travel at a combined rate of 25 miles/hour. If they need to cover 20 miles, it will take them 20/ (5/12) or roughly 48 minutes to reach one another. Either way, one minute before they collide, they will be 5/12ths of a mile away from one another, the distance they travel combined every minute. In this way, it is almost a trick question.
ANSWER B. 5/12



Current Student
Joined: 03 Apr 2013
Posts: 258
Location: India
Concentration: Marketing, Finance
GMAT 1: 740 Q50 V41
GPA: 3

Re: Two boats are heading towards each other at constant speeds
[#permalink]
Show Tags
19 Nov 2013, 12:07
Just form this simple equation : 20  (20/25 1/60)X25



Manager
Joined: 26 Sep 2013
Posts: 180
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41 GMAT 2: 730 Q49 V41

Re: Two boats are heading towards each other at constant speeds
[#permalink]
Show Tags
19 Nov 2013, 17:38
Bunuel wrote: gmihir wrote: Two boats are heading towards each other at constant speeds of 5 miles/hr and 20 miles/hr respectively. They begin at a distance 20 miles from each other. How far are they (in miles) one minute before they collide ?
A. 1/12 B. 5/12 C. 1/6 D. 1/3 E. 1/5 The question asks: how far apart will they be 1 minute=1/60 hours before they collide? Since the combined rate of the boats is 5+20=25 mph then 1/60 hours before they collide they'll be rate*time=distance > 25*1/60=5/12 miles apart. Answer: B. Similar question to practice: 12easypiecesornot126366.html#p1033924Hope it helps. Can you tell me why my method didn't work: I figured that 5*T+20*T=20 (since they'll have traveled 20 miles combined when they collide). so 25T=20, thus T=4/5. So if they collide at the 48 minute mark, then the distance they travel in 44 minutes combined, subtracted from 20 should give you the answer. so 5*(47/60)+20*(47/60)=D 235/60+940/60=D 1175/60=D 19 \(\frac{35}{60}\)=D So if they had traveled 19 35/60 miles in 44 minutes combined, then one minute before they collide they should be 25/60 miles apart. EDIT: Just edited my work. I had a glaring error. My method did work. I keep doing this. I don't know what's happening to me. I'm starting to become concerned. I make errors in calculations on roughtly 80% of the problems I do. I read the questions, and by the second line of the question my mind is already wandering and I don't see or remember anything after the first few words of the question. UGH. Just today I've done ~100 problems, and I made errors in simple addition, or just didn't remember a constraint (answer must be positive or something) on 89 of them. I feel like my brain is dying or something.



Manager
Joined: 22 Jul 2014
Posts: 120
Concentration: General Management, Finance
WE: Engineering (Energy and Utilities)

Re: Two boats are heading towards each other at constant speeds
[#permalink]
Show Tags
18 Sep 2014, 05:12
Sorry I don't get it The question states that we must find out the distance 1 min from the time of collision. So if they collided at the 48th minute, question asks us to find the distance of the 2 boats from each other in the 47th minute right?



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10784
Location: Pune, India

Re: Two boats are heading towards each other at constant speeds
[#permalink]
Show Tags
18 Sep 2014, 20:55
alphonsa wrote: Sorry I don't get it The question states that we must find out the distance 1 min from the time of collision. So if they collided at the 48th minute, question asks us to find the distance of the 2 boats from each other in the 47th minute right? Yes, there are two ways we can find the distance between the boats in the 47th minute: One way is we find the distance traveled by the boats in 47 mins and then subtract that out of the total distance. Another way is to find the distance they will cover in the last 1 min. That must be the distance between them in the 47th minute. Because at the end of the 48th minute, the boats meet  i.e. there is no distance between them. Knowing their speed, we know the distance traveled by them in 1 min and hence know the distance between them 1 min before they meet. The solutions above use this approach to get the answer.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Intern
Joined: 08 Dec 2013
Posts: 29

Re: Two boats are heading towards each other at constant speeds
[#permalink]
Show Tags
25 Oct 2014, 00:48
what is the problem with my solution
after calculating the time of collision i.e 4/5=48 mins.
since we need to calculate the distance b/w them in 47 mins,can`t we do like this ..
boat 1 48 mins=4miles 47 mins=(4/48) *47
similarly for boat 2 47 mins=(16/48)*47
then subtracting the distance of boat 2 from boat 1.. (16/48)*47(4/48) *47=answer.
kindly correct me on this.
thank you



Intern
Joined: 08 Dec 2013
Posts: 29

Re: Two boats are heading towards each other at constant speeds
[#permalink]
Show Tags
25 Oct 2014, 00:49
what is the problem with my solution
after calculating the time of collision i.e 4/5=48 mins.
since we need to calculate the distance b/w them in 47 mins,can`t we do like this ..
boat 1 48 mins=4miles 47 mins=(4/48) *47
similarly for boat 2 47 mins=(16/48)*47
then subtracting the distance of boat 2 from boat 1.. (16/48)*47(4/48) *47=answer.
kindly correct me on this.
thank you



Math Expert
Joined: 02 Sep 2009
Posts: 65785

Two boats are heading towards each other at constant speeds
[#permalink]
Show Tags
25 Oct 2014, 04:53
shreygupta3192 wrote: what is the problem with my solution
after calculating the time of collision i.e 4/5=48 mins.
since we need to calculate the distance b/w them in 47 mins,can`t we do like this ..
boat 1 48 mins=4miles 47 mins=(4/48) *47
similarly for boat 2 47 mins=(16/48)*47
then subtracting the distance of boat 2 from boat 1.. (16/48)*47(4/48) *47=answer.
kindly correct me on this.
thank you It should be \(20  ((\frac{16}{48})*47 + (\frac{4}{48}) *47)\).
_________________



Intern
Joined: 08 Dec 2013
Posts: 29

Re: Two boats are heading towards each other at constant speeds
[#permalink]
Show Tags
30 Oct 2014, 10:49
thank you for the valuable reply but why are we subtracting the total from 20 and not subtracting them by each other(as per my solution), as that will give us how far are they from each other.. confused.



Math Expert
Joined: 02 Sep 2009
Posts: 65785

Re: Two boats are heading towards each other at constant speeds
[#permalink]
Show Tags
31 Oct 2014, 05:34
shreygupta3192 wrote: thank you for the valuable reply but why are we subtracting the total from 20 and not subtracting them by each other(as per my solution), as that will give us how far are they from each other.. confused. In 47 minutes boat 1 covers (16/48)*47 = 47/3 miles and boat 2 covers (4/48) *47 = 47/12 miles. Together in 47 minutes they cover 47/3 + 47/12 = 235/12 miles. Therefore after 47 minutes, so 1 minute before they meet, they will be 20  235/12 = 5/12 miles apart. Hope it's clear. P.S. 30second approach to deal with this problem is given here: twoboatsareheadingtowardseachotheratconstantspeeds131737.html#p1080945
_________________



Intern
Joined: 08 Dec 2013
Posts: 29

Re: Two boats are heading towards each other at constant speeds
[#permalink]
Show Tags
06 Nov 2014, 00:19
okay now it`s clear. a very stupid mistake from my side. Thanx Bunuel.



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 17272
Location: United States (CA)

Two boats are heading towards each other at constant speeds
[#permalink]
Show Tags
30 Jan 2015, 12:20
In these types of Combined Rate questions, you have to stay focused on what the question asks you to figure out and what the two vehicles are doing. In this question, they two vehicles are heading TOWARDS one another, so the movement of BOTH vehicles decreases the distance between them. As such, we have to ADD their rates so that we can figure out how much the distance decreases with each passing time period (second, minute, hour, etc.). In a different type of question, you might have one vehicle chasing another. In these situations, the vehicle "in front" is moving AWAY from the vehicle "in back." So even though the "back vehicle" might be moving faster, the "front vehicle" is still moving AWAY from it. As such, we have to SUBTRACT their rates to figure out how long the "back vehicle" takes to catch up to the "front vehicle".
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Manager
Joined: 23 May 2013
Posts: 179
Location: United States
Concentration: Technology, Healthcare
GMAT 1: 760 Q49 V45
GPA: 3.5

Two boats are heading towards each other at constant speeds
[#permalink]
Show Tags
24 Jul 2015, 07:11
Another quick way to think about this: go backwards. Assume they are at the same point and are going in opposite directions. One at t/12 miles per hour and the other at t/2 miles per hour. After one minute, they are
\(\frac{1}{12} + \frac{1}{3} = \frac{15}{36} = \frac{5}{12}\) miles apart.



Intern
Joined: 05 May 2015
Posts: 5

Re: Two boats are heading towards each other at constant speeds
[#permalink]
Show Tags
24 Jul 2015, 14:18
There are some helpful and quick solutions to it but I thought of an alternate approach to solve it:
Relative speed for the boats = 5+20=25 mph Total Distance = 20 miles Time Taken=distance/speed=20/25=4/5 hrs=4*60/5=48 mins
So, One minute before the collision, the distance between those boats would be the distance traveled by these boats in 1 minute which is =20/48 miles (As it takes 48 mins to travel 20 miles so in 1 minute it would travel 20/48 miles) =5/12 miles




Re: Two boats are heading towards each other at constant speeds
[#permalink]
24 Jul 2015, 14:18



Go to page
1 2
Next
[ 27 posts ]

