Question 67

The speed of boat A in still water is 2km/h less than the speed of the boat B in still water. The time taken by boat A to travel a distance of 20km downstream is 30 minutes more than time taken by boat B to travel the same distance downstream. If the speed of the current is 1/3rd of the speed of the boat A in still water, what is the speed of boat B? (km/h)

Solution

Let speed of boat A in still water = $$3x$$

=> Speed of boat B in still water = $$(3x + 2)$$ km/hr

=> Speed of current = $$x$$ km/hr

Acc. to ques

=> $$\frac{20}{3x + x} - \frac{20}{3x + 2 + x} = \frac{1}{2}$$

=> $$\frac{5}{x} - \frac{10}{2x + 1} = \frac{1}{2}$$

=> $$\frac{10x + 5 - 10x}{x (2x + 1)} = \frac{1}{2}$$

=> $$2x^2 + x - 10 = 0$$

=> $$(2x + 5) (x - 2) = 0$$

=> $$x = 2$$

$$\therefore$$ Speed of boat B = $$3 \times 2 + 2 = 8$$ km/hr

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