Question
The stream flows at 2 km/h. A boat takes 1 hour more to
cover 36 km upstream than it takes to go 40 km downstream. What is the distance the boat can cover in still water in 5 hours?Solution
ATQ,
Let the speed of the boat in still water = ‘y’ km/h Then, upstream speed = (y – 2) km/h And, downstream speed = (y + 2) km/h According to the question, 36/(y – 2) – 40/(y + 2) = 1 (36y + 72 – 40y + 80)/(y² – 4) = 1 (–4y + 152)/(y² – 4) = 1 => –4y + 152 = y² – 4 => y² + 4y – 156 = 0 => y² + 13y – 12y – 156 = 0 => y(y + 13) – 12(y + 13) = 0 => (y – 12)(y + 13) = 0 => y = 12 or -13 Rejecting negative value, Speed in still water = 12 km/h Distance in 5 hours = 12 × 5 = 60 km
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