The current of a stream runs at the rate of 3 kmph. A boat goes 18 km and back…
2023
The current of a stream runs at the rate of 3 kmph. A boat goes 18 km and back to the starting point in 8 hours, then find the speed of the boat in still water ?
- A.
9 kmph
- B.
12 kmph
- C.
10 kmph
- D.
6 kmph
Attempted by 3 students.
Show answer & explanation
Correct answer: D
Answer: 6 kmph
Let the speed of the boat in still water be x kmph. Speed of the stream is 3 kmph, so downstream speed = x + 3 and upstream speed = x - 3.
Total time for 18 km downstream and 18 km upstream is 18/(x+3) + 18/(x-3) = 8 hours.
Multiply both sides by (x+3)(x-3): 18(x-3) + 18(x+3) = 8(x^2 - 9).
Simplify: 18x - 54 + 18x + 54 = 36x, so 36x = 8x^2 - 72. Rearranged: 8x^2 - 36x - 72 = 0. Divide by 4: 2x^2 - 9x - 18 = 0.
Solve the quadratic: Discriminant D = (-9)^2 - 4·2·(-18) = 81 + 144 = 225, so √D = 15. Thus x = (9 ± 15)/4. The positive root is x = (9 + 15)/4 = 6 kmph (the other root is negative and rejected).
Check: downstream speed 9 kmph and upstream speed 3 kmph give times 18/9 = 2 hours and 18/3 = 6 hours, total 8 hours, matching the problem statement.