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# Two boats are heading towards each other at constant speeds

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Manager
Joined: 08 May 2015
Posts: 87
GMAT 1: 630 Q39 V38
GMAT 2: 670 Q44 V38
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Re: Two boats are heading towards each other at constant speeds  [#permalink]

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07 Aug 2015, 14:02
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This is the kind of question that proves that you should not start solving the question without glancing at the answers first.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
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22 Mar 2016, 21:31
VeritasPrepKarishma wrote:
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

Responding to a pm:
Quote:
You mentioned in your comment above that "they" cover the distance of 20 miles in 48 minutes. Maybe I am misunderstaning this but how is that possible? The two boats, initially, begin at a distance of 20 miles away from each other, so isn't the 48 minutes the amount of time it will take them to "meet", and not actually cover the whole 20 miles, as you mentioned in your comment above?

The question involves relative speed and in relative speed, we often talk about the combined distance covered by two objects.

Say A and B are standing 20 feet apart. They walk toward each other and now they are 10 feet apart. "They" have covered a distance of 10 feet together. We don't know how much distance which one covered but we know that together they covered 10 feet. Say they took 1 minute to cover the 10 feet together. Then their combined speed is 10 feet per min.
Perhaps A's speed is 4 feet/ min and B's speed is 6 feet /min so that in one minute, they together covered 10 feet.
or perhaps A's speed is 8 feet/ min and B's speed is 2 feet /min so that in one minute, they together covered 10 feet.
or some other such case.

Similarly, when the boats head toward each other, they are together reducing the initial distance between them of 20 miles. When they finally meet, distance between them is 0 miles so they covered 20 miles together. Since they meet each other in 48 mins, it means their combined speed is such that they covered 20 miles in 48 mins.
Does this clarify the situation?
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Karishma
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Re: Two boats are heading towards each other at constant speeds  [#permalink]

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24 Aug 2019, 09:55
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Joined: 03 Jun 2019
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24 Aug 2019, 11:02
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

Given: 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.

Asked: How far are they (in miles) one minute before they collide ?

Relative speed = 25 kmh

Distance travelled in 1 min = 25/60 = 5/12 km

IMO B

Posted from my mobile device
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Joined: 14 May 2018
Posts: 95
Re: Two boats are heading towards each other at constant speeds  [#permalink]

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19 Sep 2019, 05:57
This question REALLLYY made my mind jog!
Are there more questions like this one I can refer to ?
Math Expert
Joined: 02 Sep 2009
Posts: 59622
Re: Two boats are heading towards each other at constant speeds  [#permalink]

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19 Sep 2019, 06:19
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Re: Two boats are heading towards each other at constant speeds   [#permalink] 19 Sep 2019, 06:19

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