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Two boats leave the same dock at the same time, one traveling due west

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Bunuel
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Two boats leave the same dock at the same time, one traveling due west [#permalink] New post   03 Dec 2020, 12:00
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65% (01:55) correct 35% (01:31) wrong based on 46 sessions
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Two boats leave the same dock at the same time, one traveling due west at 8 miles per hour and the other due north at 15 miles per hour. How many miles apart are the boats after three hours?

(A) 17
(B) 39
(C) 51
(D) 69
(E) 75
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C
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Biswadeep20
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Re: Two boats leave the same dock at the same time, one traveling due west [#permalink] New post   03 Dec 2020, 12:15
One boat is traveling Northwards at 15 miles per hour. The other one Westwards at 8 miles per hour.

In 3 hours, the northern boat has covered 45 miles and the western boat has covered 24 miles. So the distance between them is the hypotenuse of the two directions. We can reduce the values to 15 and 8 while calculating, resulting 17 as the end result. Hence, the final result is 51(17*3).
Answer C is the correct choice.

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Re: Two boats leave the same dock at the same time, one traveling due west [#permalink] New post   03 Dec 2020, 20:01
IMO C

the 2 ships travelling north and west will form the two sides of a right angled triangle.
Pythagorean triplet being used (8, 15, 17)

after 3 hours the two sides will be of size: 24 (speed * time = 8*3) and 45(speed * time = 15*3)
=>multiplying the Pythagorean triplet by 3 (8*3, 15*3, 17*3)

=> distance between the boats = 17*3 = 51
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Re: Two boats leave the same dock at the same time, one traveling due west [#permalink] New post   06 Dec 2020, 09:17
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Bunuel wrote:
Two boats leave the same dock at the same time, one traveling due west at 8 miles per hour and the other due north at 15 miles per hour. How many miles apart are the boats after three hours?

(A) 17
(B) 39
(C) 51
(D) 69
(E) 75

Solution:

The distances traveled by the two boats and the distance between the two boats form a right triangle. If we let x = the distance between the two boats after three hours, we can create the equation:

[8(3)]^2 + [15(3)]^2 = x^2

However, without actually solving the equation, we can see that if the boats travel for only one hour, the distance between them will be 17 miles, since the distances traveled by the two boats and the distance between the two boats always form a 8-15-17 right triangle. Therefore, after 3 hours, the distance between two boats is 17(3) = 51 miles.

Answer: C
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Re: Two boats leave the same dock at the same time, one traveling due west [#permalink]
06 Dec 2020, 09:17
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