Multiple choice

A speedboat travels at a speed of s kilometers per hour in still water and moves directly upstream and downstream along the center of a straight canal. The boat's speed relative to the bank depends only on the speed and direction of the current. What is the value of s? (1) It takes the same amount of time for the boat to travel 6 kilometers downstream as it takes to travel 4 kilometers upstream. (2) The current flows downstream at a constant speed of 1.5 kilometers per hour.

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
C Correct answer
AI explanation

Statement one establishes the ratio of the boat's downstream and upstream speeds, giving the equation 6 / (s + c) = 4 / (s - c) where c is the current's speed, which simplifies to s = 5c. Statement two alone only provides the value of the current's speed (c = 1.5), which is insufficient without the boat's speed. By substituting c = 1.5 into the first equation, we find the still water speed s = 5 * 1.5 = 7.5 km/hr, proving both statements together are sufficient.

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