Multiple choice

A boat goes $24$ km upstream and $28$ km downstream in $6$ hours. It goes $30$ km upstream and $21$ km downstream in $6$ hours and $30$ minutes. The speed of the boat on still water is

  1. $8$ km/hr
  2. $9$ km/hr
  3. $12$ km/hr
  4. $10$ km/hr
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let u be upstream speed and v be downstream speed. 24/u + 28/v = 6; 30/u + 21/v = 6.5. Let x=1/u, y=1/v. 24x + 28y = 6; 30x + 21y = 6.5. Multiply first by 3, second by 4: 72x + 84y = 18; 120x + 84y = 26. Subtract: 48x = 8 => x = 1/6. So u = 6. 24(1/6) + 28y = 6 => 4 + 28y = 6 => 28y = 2 => y = 1/14. So v = 14. Still water speed = (u+v)/2 = (6+14)/2 = 10 km/hr.

AI explanation

Let the upstream speed be x and the downstream speed be y. The equations from the given times are 24/x + 28/y = 6 and 30/x + 21/y = 6.5. Multiplying the first equation by 5 and the second by 4 gives 120/x + 140/y = 30 and 120/x + 84/y = 26. Subtracting the second from the first yields 56/y = 4, so y = 14. Substituting y back into the first equation gives 24/x + 2 = 6, making x = 6. The speed of the boat in still water is (14 + 6) / 2 = 10 km/hr. The result is 10 km/hr.

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