A motorboat covers a certain distance downstream in a river in five hours. It covers the same distance upstream in river in six hours. The speed of water is 2 km/h. Find the speed of the boat in still water.
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Answers
Step-by-step explanation:
let the speed of motor boat = x km /h
upstream distance = downstream distance
5(x+2) = 6(x-2)
5x+10=6x-12
5x-6x= -12-10
-x = -22
( both the signs of - will be cancelled out)
Answer : speed of motor boat= 22km/h
Solution :
Let the speed of the boat in still water be x km/h.
Speed of water = 2 km/h
Speed of the boat downstream = (x + 2) km/h
Distance covered in 5 hours = Speed × Time
= 5(x + 2) km
[ The relative speed when the direction of the boat and the flow of water is the same = The sum of the speeds of the boat and water ]
Speed of the boat upstream = (x – 2) km/h
Distance covered in 6 hours = Speed × Time
= 6(x – 2) km
[The relative speed when the boat travels opposite to the flow of water = The difference in the speeds of the boat and water]
But the boat covers the same distance upstream and downstream.
Therefore,
6(x – 2) = 5(x + 2)
6x – 12 = 5x + 10
6x – 5x = 12 + 10
x = 22
Hence, the speed of the boat in still water = 22 km/h.
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Check :
Distance covered in 5 hours (downstream)
= Speed × Time
= 5(22 + 2) = 120 km
Distance covered in 6 hours (upstream)
= Speed × Time
= 6(22 – 2) = 120 km
In both the cases, the distance is found to be the same.
Hence, the solution is correct.
_______________________
Answer :
the speed of the boat in still water = 22 km/h.