Multiple choice

A man can swim at 4.5 km/hr in still water, but takes twice as long to swim a certain distance upstream than downstream. The speed (in km/hr) of the stream is

  1. 3

  2. 7.5

  3. 2.25

  4. 1.5
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D Correct answer
Explanation

Let v be the boat speed (4.5) and s be the stream speed. Downstream speed is 4.5+s, upstream is 4.5-s. Time is distance/speed. Given 1/(4.5-s) = 2 * 1/(4.5+s), we get 4.5+s = 9-2s, so 3s = 4.5, s = 1.5.

AI explanation

Let the speed of the stream be y km/hr, so the man's upstream speed is (4.5 - y) km/hr and his downstream speed is (4.5 + y) km/hr. Because he takes twice as long to swim upstream, his upstream speed is half of his downstream speed, giving the equation 4.5 - y = (4.5 + y)/2. Multiplying both sides by 2 gives 9 - 2y = 4.5 + y, so 3y = 4.5 and y = 1.5 km/hr.

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