Multiple choice

The following problem consists of a question and two statements numbered 1 and 2. You have to decide whether the data provided in the statements is sufficient to answer the question. Rahim is riding upstream on a boat, from point A to B, at a constant speed. The distance from A to B is 30 km. One minute after Rahim leaves from point A, a speedboat starts from point A to go to point B. It crosses Rahim's boat after 4 minutes. If the speed of the speedboat is constant from A to B, what is Rahim's speed in still water? 1. The speed of the speedboat in still water is 30 km/hour. 2. Rahim takes three hours to reach point B from point A.

  1. Statement 1 alone is sufficient to answer the question, but statement 2 alone is not sufficient.

  2. Statement 2 alone is sufficient to answer the question, but statement 1 alone is not sufficient.

  3. Each statement alone is sufficient.

  4. Both statements together are sufficient, but neither of them alone is sufficient.

  5. Statements 1 & 2 together are not sufficient.
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D Correct answer
AI explanation

Let Rahim's upstream speed be x kilometers per hour and the speedboat's upstream speed be y. Based on the meeting point, we know that the speedboat travels for 4 minutes while Rahim travels for 5 minutes, leading to the equation 4y equals 5x. Statement one provides the speedboat's speed in still water as 30 km/hr, but without knowing the stream speed, we cannot find its upstream speed y to solve for x. Statement two gives Rahim's total time to travel 30 km as 3 hours, meaning his upstream speed is 10 km/hr, but we still need the speedboat's upstream speed to find its still water speed. By using statement two to establish x equals 10 and statement one to establish y equals 30 minus the stream speed, we can solve the meeting equation to find the stream speed and ultimately Rahim's speed in still water. Therefore, both statements together are sufficient.

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