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Two boats are heading towards each other at constant speeds

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Two boats are heading towards each other at constant speeds [#permalink] New post 01 May 2012, 20:29
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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
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Re: Two boats are heading towards each other at constant speeds [#permalink] New post 01 May 2012, 21:52
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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: 12-easy-pieces-or-not-126366.html#p1033924

Hope it helps.
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Re: Two boats are heading towards each other at constant speeds [#permalink] New post 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 ?
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Re: Two boats are heading towards each other at constant speeds [#permalink] New post 03 May 2012, 11:23
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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.
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Re: Two boats are heading towards each other at constant speeds [#permalink] New post 03 May 2012, 18:47
I first calculated the time at which they collide, assuming they started at the same time. but i did not even need it.

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Re: Two boats are heading towards each other at constant speeds [#permalink] New post 04 May 2012, 19:44
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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
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Re: Two boats are heading towards each other at constant speeds [#permalink] New post 25 Aug 2012, 10:53
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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.
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Re: Two boats are heading towards each other at constant speeds [#permalink] New post 06 Nov 2013, 14:47
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Re: Two boats are heading towards each other at constant speeds [#permalink] New post 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
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Re: Two boats are heading towards each other at constant speeds [#permalink] New post 19 Nov 2013, 12:07
Just form this simple equation :-

20 - (20/25 -1/60)X25

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Re: Two boats are heading towards each other at constant speeds [#permalink] New post 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: 12-easy-pieces-or-not-126366.html#p1033924

Hope 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.
Re: Two boats are heading towards each other at constant speeds   [#permalink] 19 Nov 2013, 17:38
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