A motorboat, which is set to travel at \(k\) kilometers per hour in still water, travels directly up and down the center

[Vincen]

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.

[spoiler]OA=C[/spoiler]

Source: GMAT Prep

[Brent@GMATPrepNow]

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.

[spoiler]OA=C[/spoiler]

Source: GMAT Prep

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