The speed of stream is $\frac{4{5}$ of the speed of a boat in still water. If the boat covers 198 km in 11 hours downstream, then find the difference of time taken by boat to cover 60 km in upstream and 36 km downstream.}
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Use: Downstream speed = boat + stream speed; Upstream speed = boat - stream speed. Time = Distance / Speed. Find 's' from given data, then calculate times.
Let the speed of the boat in still water be $5s$ km/h. The speed of the stream is $\frac{4}{5} \times 5s = 4s$ km/h. - The downstream speed is the sum of the boat speed and stream speed: $5s + 4s = 9s$ km/h. - The downstream distance is 198 km, covered in 11 hours. Therefore: \[9s = \frac{198}{11} = 18 \implies s = 2\] - Consequently, Boat speed = $5s = 10$ km/h, Stream speed = $4s = 8$ km/h. - The upstream speed is the difference between the boat speed and stream speed: $10 - 8 = 2$ km/h. - The time required to travel 60 km upstream is $\frac{60}{2} = 30$ hours. - The time required to travel 36 km downstream is $\frac{36}{10+8} = \frac{36}{18} = 2$ hours. - The difference in time is $30 - 2 = 28$ hours.