Multiple choice

A boat travels at a speed of 21 miles/hour in still water. The ratio of the speed of the boat upstream to the speed downstream is 2 : 5. Determine the additional time it takes for the boat to travel 72 miles upstream compared to the time it takes to travel the same distance downstream.

  1. 2 hours and 24 minutes

  2. 3 hours and 36 minutes

  3. 4 hours and 46 minutes

  4. 5 hours and 12 minutes

  5. 5 hours and 15 minutes
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let boat speed be B=21 and current speed be C. Upstream speed (B-C) / Downstream speed (B+C) = 2/5. Solving 5(21-C) = 2(21+C) gives 105-5C = 42+2C, so 7C=63, C=9. Upstream speed = 12, Downstream = 30. Time upstream = 72/12 = 6 hours. Time downstream = 72/30 = 2.4 hours. Difference = 3.6 hours, which is 3 hours 36 minutes.

AI explanation

Given the upstream to downstream speed ratio is 2:5 and the boat's still water speed is 21 mph, we use the relation that the ratio of upstream to downstream speed equals (b-c):(b+c). Letting 2x = 21-c and 5x = 21+c, adding the equations yields 7x = 42, so x = 6; this gives the upstream speed as 12 mph and the downstream speed as 30 mph. The time to travel 72 miles upstream is 72/12 = 6 hours, while downstream it is 72/30 = 2.4 hours, which is 2 hours and 24 minutes. The additional time taken is 6 minus 2.4, equaling 3.6 hours, or 3 hours and 36 minutes.

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