a steamer goes downstream from one port to another in 6 hours. it goes upstream in 7 hours. if the speed of the stream be 2 km/hr. find the speed of steamer in still water.
Answers
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★Speed of the steamer=26 km/hr
Step-by-step explanation:
Given :
• Steamer goes downstream in 6 hours
• Steamer goes upstream in 7 hours
•speed of the stream = 2 km/hr
To Find:
•Speed of the steamer in still water
Solution :
➡Here we are given that the steamer
covers same distance downstream and
upstream in 6 and 7 hours respectively.
➡Let the speed of the steamer in still water
be x km/hr.
➡Hence,
Speed while travelling upstream = (x - 2)
km/hr
Speed while travelling downstream = (x +2) km/hr
➡Now we know that,
Distance Speed x Time
➡Hence in the first case,
Distance travelled = (x + 2) × 6 ------(1)
➡Now in the second case,
Distance travelled = (x - 2) × 7 ---(2)
➡From given we know that the LHS of
equation 1 and equation 2 are equal.
➡Hence,
6 (x + 2) = 7 (x - 2)
6x + 12 = 7x - 14
7x-6x = 12 + 14
x = 26
➡But we know that
x = Speed of the steamer in still water
➡Hence speed of the steamer is 26 km/hr