Question

A boat goes 36 km downstream and comes back to the starting point 3 hours. If the speed of the current is 3 km/hr, then the speed of the boat in steel water is k times the speed of current. What is the value of k?

Answer 1

Answer:

Let the speed of boat in still water be x km/hr then,

\frac{12}{x+3}+\frac{12}{x-3} = 3

=> 12\left ( \frac{x-3+x+3}{(x+3)(x-3)} \right ) = 3

=> 4\times 2x = x^{2}-9

=> x^{2}-8x-9 = 0

=> x^{2}-9x+x-9 = 0

=> x(x-9)+1(x-9) = 0

=> (x-9)(x+1) = 0

=> x = 9, x\neq -1. Because speed cannot be negative.

Hence speed of boat in still water is 9 km/hr.

So, k = 9.

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