Multiple choice

The speed of a stream is 3 km/hr. A boat goes 36 km and comes back to the starting point in 9 hours. What is the speed (in km/hr) of the boat in still water?

  1. 8

  2. 9

  3. 10

  4. 7
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let v be the speed in still water. Upstream speed = v-3, downstream = v+3. Time = 36/(v-3) + 36/(v+3) = 9. Divide by 9: 4/(v-3) + 4/(v+3) = 1. 4(v+3) + 4(v-3) = (v-3)(v+3). 4v + 12 + 4v - 12 = v^2 - 9. 8v = v^2 - 9. v^2 - 8v - 9 = 0. (v-9)(v+1) = 0. v = 9.

AI explanation

Let the speed of the boat in still water be x, making the downstream speed x plus 3 and the upstream speed x minus 3. The total time for the 36 km round trip is 9 hours, so the equation is 36 divided by (x plus 3) plus 36 divided by (x minus 3) equals 9. Factoring out 36 gives 36 multiplied by the quantity ((x minus 3) plus (x plus 3)) divided by the quantity (x squared minus 9), which simplifies to 72x divided by (x squared minus 9) equals 9. Dividing both sides by 9 and cross-multiplying yields 8x equals x squared minus 9, or x squared minus 8x minus 9 equals 0. Factoring this quadratic equation gives (x minus 9)(x plus 1) equals 0, so the positive speed is 9 km/hr.

Keep practicing — related questions