Question
The speed of boat 'Y' in still
water is the same as the downstream speed of boat 'X'. Boat 'X' requires 1 hour longer than boat 'Y' to travel 80 km downstream. If the speed of the current is 4 km/hr, what is the speed of boat 'Y' in still water?Solution
ATQ, Let the speed of boat 'X' in still water be ‘a’ km/hr Downstream speed of boat X = ‘a + 4’ km/hr Speed of boat Y in still water = (a + 4) km/hr According to the question, 80/(a + 4) – 80/(a + 4 + 4) = 1 Or, a2 + 12a – 288 = 0 Or, a2 + 24a – 12a – 288 = 0 Or, a(a + 24) – 12(a + 24) = 0 Or, (a – 12)(a + 24) = 0 Therefore, a = 12, -24 Speed cannot be negative Therefore, speed of boat X in still water = 12 km/hr Speed of boat Y in still water = 12 + 4 = 16 km/hr
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