Multiple choice

A motor boat can travel $30\ km$ upstream and $28\ km$ downstream in $7$ hours. It can travel $21\ km$ upstream and return in $5$ hours. Find the speed of the boat in still water in $km/h$.

  1. $3$
  2. $15$
  3. $10$
  4. $11$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let u be upstream speed and v be downstream speed. 30/u + 28/v = 7 and 21/u + 21/v = 5. From the second, 1/u + 1/v = 5/21. Let x = 1/u, y = 1/v. 30x + 28y = 7 and 21x + 21y = 5 (or x + y = 5/21). Substituting y = 5/21 - x: 30x + 28(5/21 - x) = 7 => 2x + 20/3 = 7 => 2x = 1/3 => x = 1/6. So u = 6. Then y = 5/21 - 1/6 = (10-7)/42 = 3/42 = 1/14. So v = 14. Speed of boat = (u + v) / 2 = (6 + 14) / 2 = 10 km/h.

AI explanation

Let the upstream speed be x and the downstream speed be y. The equations are 30/x + 28/y = 7 and 21/x + 21/y = 5. Multiplying the second equation by 4/3 gives 28/x + 28/y = 20/3. Subtracting this from the first equation yields 2/x = 1/3, making x = 6. Substituting x into the second equation gives 21/6 + 21/y = 5, so 21/y = 1.5 and y = 14. The speed of the boat in still water is (14 + 6) / 2 = 10 km/h. The result is 10.

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