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A motorboat, which is set to travel at k kilometers per hour in still
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23 May 2020, 08:33
23 May 2020, 08:33
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A motorboat, which is set to travel at k kilometers per hour in still water, travels directly up and down the center of a straight river so that the change in the boat’s speed relative to the shore depends only on the speed and direction of the current. What is the value of k ?
(1) It takes the same amount of time for the boat to travel 4 kilometers directly downstream as it takes for it to travel 3 kilometers directly upstream.
(2) The current flows directly downstream at a constant rate of 2.5 kilometers per hour.
ID: 700119
DS20393
(1) It takes the same amount of time for the boat to travel 4 kilometers directly downstream as it takes for it to travel 3 kilometers directly upstream.
(2) The current flows directly downstream at a constant rate of 2.5 kilometers per hour.
ID: 700119
DS20393
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Joined: 12 Sep 2015
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Location: Canada
Re: A motorboat, which is set to travel at k kilometers per hour in still
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23 May 2020, 10:24
23 May 2020, 10:24
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Bunuel wrote:
A motorboat, which is set to travel at k kilometers per hour in still water, travels directly up and down the center of a straight river so that the change in the boat’s speed relative to the shore depends only on the speed and direction of the current. What is the value of k ?
(1) It takes the same amount of time for the boat to travel 4 kilometers directly downstream as it takes for it to travel 3 kilometers directly upstream.
(2) The current flows directly downstream at a constant rate of 2.5 kilometers per hour.
DS20393
(1) It takes the same amount of time for the boat to travel 4 kilometers directly downstream as it takes for it to travel 3 kilometers directly upstream.
(2) The current flows directly downstream at a constant rate of 2.5 kilometers per hour.
DS20393
Target question: What is the value of k ?
Given: A motorboat, which is set to travel at k kilometers per hour in still water, travels directly up and down the center of a straight river so that the change in the boat’s speed relative to the shore depends only on the speed and direction of the current.
Let c = the speed of the CURRENT
So, k + c = the boat’s DOWNSTREAM speed relative to the shore
And k - c = the boat’s UPSTREAM speed relative to the shore
Statement 1: It takes the same amount of time for the boat to travel 4 kilometers directly downstream as it takes for it to travel 3 kilometers directly upstream.
Time = distance/speed
So, we can write: 4/(k + c) = 3/(k - c)
Cross multiply to get: (4)(k - c) = (3)(k + c)
Expand: 4k - 4c = 3k + 3c
Subtract 3k from both sides: k - 4c = 3c
Add 4c to both sides: k = 7c
So the value of k depends on the value of c.
Since we don't know the value of c, there's no way to determine the value of k
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The current flows directly downstream at a constant rate of 2.5 kilometers per hour.
Knowing only the speed of the current does not provide enough information to determine the value of k
Statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 indirectly tells us that k = 7c
Statement 2 tells us that c = 2.5
We get: k = 7c = 7(2.5) = 17.5
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
General Discussion
Re: A motorboat, which is set to travel at k kilometers per hour in still
[#permalink]
23 May 2020, 10:30
23 May 2020, 10:30
Statement 1-
Speed of the boat while going downstream = k+x, where x is the speed of the current
Speed of the boat while going upstream = k-x
\(\frac{k+x}{k-x }= \frac{4}{3}\)
1 equation and 2 unknowns
Insufficient
Statement 2 -
x = 2.5
1 equation and 2 unknowns
Insufficient
Combining 2 statements
2 equation and 2 unknowns
Sufficient
Speed of the boat while going downstream = k+x, where x is the speed of the current
Speed of the boat while going upstream = k-x
\(\frac{k+x}{k-x }= \frac{4}{3}\)
1 equation and 2 unknowns
Insufficient
Statement 2 -
x = 2.5
1 equation and 2 unknowns
Insufficient
Combining 2 statements
2 equation and 2 unknowns
Sufficient
Bunuel wrote:
A motorboat, which is set to travel at k kilometers per hour in still water, travels directly up and down the center of a straight river so that the change in the boat’s speed relative to the shore depends only on the speed and direction of the current. What is the value of k ?
(1) It takes the same amount of time for the boat to travel 4 kilometers directly downstream as it takes for it to travel 3 kilometers directly upstream.
(2) The current flows directly downstream at a constant rate of 2.5 kilometers per hour.
DS20393
(1) It takes the same amount of time for the boat to travel 4 kilometers directly downstream as it takes for it to travel 3 kilometers directly upstream.
(2) The current flows directly downstream at a constant rate of 2.5 kilometers per hour.
DS20393
