Question
A boat travelling downstream travels at a speed which is
25% faster than it travels in water that is still. Determine how long it takes the boat to travel 135 km both upstream and downstream assuming it can go 216 km upstream and 180 km downstream in 12 hours.Solution
ATQ, Let's assume the boat travels at "4y" km/h in still water. Boat speed downstream = 1.25 × 4y = 5y km/h Stream speed equals 5y – 4y = y km/h. Boat speed upstream is equal to 4y – y = 3y km/h. ATQ, 216/3x + 180/5x = 12 Or, 72/x + 36/x = 12 Or, x = (72 + 36)/12 = 9 Boat speed downstream is 5 × 9 = 45 km/h. Boat speed upstream is equal to 3 × 9 = 27 km/h. (135/27) + (135/45) = 5 + 3 = 8 hours is the desired time.
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