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# Two boats, traveling at 5 and 10 km per hour

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Intern
Joined: 26 Sep 2018
Posts: 10
Two boats, traveling at 5 and 10 km per hour  [#permalink]

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01 Nov 2018, 05:57
3
00:00

Difficulty:

45% (medium)

Question Stats:

65% (02:02) correct 35% (02:27) wrong based on 90 sessions

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Two boats, traveling at 5 and 10 km per hour, head directly towards each other. They begin at a distance of 20 km from each other. How far apart are they (in km) one minute before they collide.

a. $$\frac{1}{12}$$
b. $$\frac{1}{6}$$
c. $$\frac{1}{4}$$
d. $$\frac{1}{3}$$
e. $$\frac{1}{5}$$
Manager
Joined: 24 Dec 2017
Posts: 185
Location: India
Concentration: Strategy, Real Estate
Schools: Johnson '21
Re: Two boats, traveling at 5 and 10 km per hour  [#permalink]

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01 Nov 2018, 07:17
1
Boat A = 5 km/hour
=>5/60 = 1/12 in 1 minute

Boat B = 10 km/hour
=>10/60 = 1/6 in 1 minute

One minute before they collide
=>1/12 + 1/6
=>(1+2)/12
=>3/12
=>1/4 kms apart

IMO C
Intern
Joined: 07 Feb 2017
Posts: 25
Re: Two boats, traveling at 5 and 10 km per hour  [#permalink]

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02 Nov 2018, 07:32
1
1
1
RhythmGMAT wrote:
Two boats, traveling at 5 and 10 km per hour, head directly towards each other. They begin at a distance of 20 km from each other. How far apart are they (in km) one minute before they collide.

a. $$\frac{1}{12}$$
b. $$\frac{1}{6}$$
c. $$\frac{1}{4}$$
d. $$\frac{1}{3}$$
e. $$\frac{1}{5}$$

There is a logical way to solve.

Total time taken by both boats to collide = 20/(5+10) = 4/3 hr or 80 min

Distance covered per minute = 20/80 = 1/4 km/min

so on the 79th minute, they will be 1/4 th of km away from each other.
Manager
Joined: 08 Sep 2008
Posts: 134
Location: India
Concentration: Operations, General Management
Schools: ISB '20
GPA: 3.8
WE: Operations (Transportation)
Re: Two boats, traveling at 5 and 10 km per hour  [#permalink]

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02 Nov 2018, 07:47
1
Its simple:

Resultant speed: 10+5= 15 km/h
Distance travel in 1 minute: 15/60= 1/4

C.
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Re: Two boats, traveling at 5 and 10 km per hour  [#permalink]

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03 Nov 2018, 17:54
RhythmGMAT wrote:
Two boats, traveling at 5 and 10 km per hour, head directly towards each other. They begin at a distance of 20 km from each other. How far apart are they (in km) one minute before they collide.

a. $$\frac{1}{12}$$
b. $$\frac{1}{6}$$
c. $$\frac{1}{4}$$
d. $$\frac{1}{3}$$
e. $$\frac{1}{5}$$

The distance between the two boats one minute before they collide is precisely the combined amount of distance traveled by each of the boats in one minute. In one minute, the first boat travels 5 x 1/60 = 5/60 km and the second boat travels 10 x 1/60 = 10/60 km. Therefore, one minute before the collide, they are 5/60 + 10/60 = 15/60 = 1/4 km apart.

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Re: Two boats, traveling at 5 and 10 km per hour   [#permalink] 03 Nov 2018, 17:54
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