Multiple choice

The total time taken by a boat to travel 55 km upstream and return to the starting point is 16 hours. If the speed of the stream is 3 km/hr, then what is the speed of the boat in still water?

  1. 6 km/hr

  2. 7 km/hr

  3. 8 km/hr

  4. 8.5 km/hr

  5. 9 km/hr
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C Correct answer
Explanation

Let v be the speed of the boat. Upstream speed = v - 3, downstream speed = v + 3. Time equation: 55/(v-3) + 55/(v+3) = 16. Solving 55(v+3 + v-3) / (v^2 - 9) = 16 gives 110v = 16(v^2 - 9). 16v^2 - 110v - 144 = 0. Dividing by 2: 8v^2 - 55v - 72 = 0. Factoring gives (v - 8)(8v + 9) = 0, so v = 8.

AI explanation

Let the speed of the boat in still water be x km/hr, making the upstream speed x minus 3 and the downstream speed x plus 3. Using the formula Time equals Distance divided by Speed, the total time is 55 divided by x minus 3 plus 55 divided by x plus 3, which equals 16. Multiplying by the common denominator gives 55x plus 165 plus 55x minus 165 equals 16x squared minus 144. Simplifying this yields the quadratic equation 16x squared minus 110x minus 144 equals 0, and dividing by 2 gives 8x squared minus 55x minus 72 equals 0, which factors to x equals 8 as the positive root, making the speed of the boat 8 km/hr.

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