Question
A steamer goes downstream from one port to another in 9 hours. It covers the same distance upstream in 10 hours. If the speed of the stream be 1km/ h, find the speed of the steamer in still water and the distance between the ports.
✓
Answer
Let the speed of the steamer in still water be x km/ h.
Speed (downstream) = (x + 1)km/ h
Speed (upstream) = (x - 1) km/h
Distance covered in 9 hours while going downstream = 9( x + 1 )km
Distance covered in 10 hours while going upstream = 10( x - 1 )km
But both of these distances will be same.
9 (x + 1) = 10 (x - 1)
⇒ 9x + 9 = 10x - 10
⇒ 9 + 10 = 10x − 9x
⇒ 19 = x
⇒ x = 19
Therefore, the speed of the steamer in still water is 19 km/ h.
Distance between the ports = 9(x + 1) = 9(19 + 1) = 9 × 20 = 180km
Speed (downstream) = (x + 1)km/ h
Speed (upstream) = (x - 1) km/h
Distance covered in 9 hours while going downstream = 9( x + 1 )km
Distance covered in 10 hours while going upstream = 10( x - 1 )km
But both of these distances will be same.
9 (x + 1) = 10 (x - 1)
⇒ 9x + 9 = 10x - 10
⇒ 9 + 10 = 10x − 9x
⇒ 19 = x
⇒ x = 19
Therefore, the speed of the steamer in still water is 19 km/ h.
Distance between the ports = 9(x + 1) = 9(19 + 1) = 9 × 20 = 180km
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