Question
A boat’s speed in still water is 1.5 times the speed of the current. It takes the boat 22.5 hours to travel 90 km upstream. If the current’s speed were increased by 4 km/hr, the boat would take 5 hours to travel "k" kilometers downstream. Calculate the value of "k".
Solution
ATQ, Let the speed of the current be 'p' km/hr Therefore, speed of the boat in still water = 1.5p km/hr According to the question, 90/(1.5p – p) = 22.5 Or, 0.5p = 4 Or, p = 8 km/hr Therefore, speed of current = p = 8 km/hr Therefore, speed of boat in still water = 1.5p = 12 km/hr According to the question, New speed of the current = (8 + 4) = 12 km/hr Therefore, downstream speed of the boat = 12 + 12 = 24 km/hr Downstream distance covered in 5 hours = 24 × 5 = 120 km
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