Question

A man swimming in a stream which flows at \( 1 \frac{1}{2} \) km/hr finds that in a given time he can swim twice as far with the stream as he can against it. At what rate does he swim?

• A. \( 4 \frac{1}{2} \) km/hr
• B. \( 5 \frac{1}{2} \) km/hr
• C. \( 7 \frac{1}{2} \) km/hr
• D. None of these

Hint:

For boat and stream problems, use the ratio of distances or times to form equations and solve for the still water speed.

Answer 1

The Correct Option is A

Let the swimmer's speed in still water be \( x \) km/hr.
The speed downstream (with the stream): \[ x + 1.5 \] The speed upstream (against the stream): \[ x - 1.5 \] Given that the distance covered downstream is twice that covered upstream in the same time: \[ \frac{x + 1.5}{x - 1.5} = 2 \] Cross multiplying: \[ x + 1.5 = 2(x - 1.5) \] \[ x + 1.5 = 2x - 3 \] \[ 1.5 + 3 = 2x - x \] \[ 4.5 = x \] Thus, the speed of the swimmer is \( 4 \frac{1}{2} \) km/hr.