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boats

by shashank.ism » Tue Feb 09, 2010 1:13 pm
Two boats, traveling at 5 and 10 kms per hour, head directly towards each other. They begin at a distance of 20 kms from each other. How far apart are they (in kms) one minute before they collide?


1/12
1/6
1/4
1/3
1/8

[spoiler]Correct Answer: c[/spoiler]
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by papgust » Tue Feb 09, 2010 6:21 pm
Relative speed = 5+10 = 15 kms/hr

Time taken at which 2 boats collide is after = 20/15 = 4/3 = 1 hr 20 min (or) 80 min

1 min before, distance covered is
20 - 20*60/79 = 20 - (~ 15 kms) = 5 kms or 1/4th of the total distance.
Last edited by papgust on Tue Feb 09, 2010 9:52 pm, edited 1 time in total.
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by Stuart@KaplanGMAT » Tue Feb 09, 2010 7:40 pm
papgust wrote:Relative speed = 5+10 = 15 kms/hr

Time taken at which 2 boats collide is after = 20/15 = 4/3 = 1 hr 20 min (or) 79 min

1 min before, distance covered is
20 - 20*60/79 = 20 - (~ 15 kms) = 5 kms or 1/4th of the total distance.
The answer is 1/4 of a km, not 1/4 of the total distance.

We can answer this question very quickly if we understand relative rates.

Here's the rule to apply:

When two objects are moving in opposite directions, ADD the rates to get the total rate.

As Papgust noted, the total rate is 15kph.

Now, when the two objects collide in a ball of fire, d=0. To solve the question we simply need to figure out how far they travelled in that final minute.

t = 1/60
r = 15
d = r*t = 1/60 * 15 = 15/60 = 1/4 of a km... choose C.
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