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]

01 May 2012, 21:29

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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]

01 May 2012, 22:52

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gmihir wrote:

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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Intern

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Re: Two boats are heading towards each other at constant speeds [#permalink]

02 May 2012, 22:34

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]

03 May 2012, 12:23

gmihir wrote:

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]

03 May 2012, 19:47

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]

04 May 2012, 20:44

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gmihir wrote:

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]

25 Aug 2012, 11:53

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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] 25 Aug 2012, 11:53

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Two boats are heading towards each other at constant speeds

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