A steamer goes downstream from one point to another in 9 hours.It cover the same distance upstream in 10 hours.If the speed of the stream be 1km/he,find the speed of the steamer in still water and the distance between the ports.................
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Answers
Step-by-step explanation:
Given, speed of the stream = 1 km/hr
Let the speed of steamer in still water be xkm/hr.
Speed of the steamer downstream = Speed of steamer in still water + Speed of the stream = (x + 1) km/hr
Speed of the steamer upstream = Speed of steamer in still water – Speed of the stream = (x – 1) km/hr
Distance covered by the steamer downstream in 9 hours = 9 (x + 1) km (. :
Distance = Speed × Time)
Distance covered by the steamer upstream in 10 hours = 10 (x – 1) km.
Distance covered by steamer downstream in 9 hours = Distance covered by steamer upstream in 10 hours
∴ 9 (x + 1) = 10 (x – 1)
⇒ 9x + 9 = 10x – 10
⇒ 9x – 10 = – 10 – 9
⇒ – x = – 19
⇒ x = 19
∴ Speed of steamer in still water is 19 km/hr.
Distance between the two ports = 9 (x + 1) km = 9 (19 +1) km = 9 × 20 km = 180 km