Question
The boat's speed in still water
is 20% greater than the speed of the stream. If it takes the boat 4 hours more to travel 176 km downstream than it does to travel 8 km upstream, what is the time required for the boat to travel 264 km downstream and 16 km upstream?Solution
ATQ, Let the speed of the stream be 'a' km/hr Therefore, speed of the boat in still water = 1.20 × a = '1.2a' km/hr Downstream speed of the boat = 1.2a + a = '2.2a' km/hr Upstream speed of the boat = 1.2a - a = '0.2a' km/hr According to the question, (176/2.2a) - (8/0.2a) = 4 Or, (80/a) - (40/a) = 4 Or, 4a = 40 Or, 'a' = (40/4) = 10 Therefore, downstream speed of the boat = 2.2a = 2.2 × 10 = 22 km/hr Upstream speed of the boat = 0.2a = 0.2 × 10 = 2 km/hr Required time taken = (264/22) + (16/2) = 12 + 8 = 20 hours
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