the speed of river current is 5 km/h. A boat takes the same time to travel 8 km upstream as it does to travel 12 km downstream. Find the boat's speed in still water.
Answers
Answered by
45
Let the speed of boat in still water be x km/h
Now
In Upstream, we know that
Speed of Boat = Speed of boat in still water - speed of river current
∴ Speed of boat in upstream = x - 5
Distance in upstream = 8 km
∴ Time taken in upstream = 8/(x-5) [Time = distance/speed] --- ( i )
In Downstream
Speed of boat = Speed of boat in still water + speed of river current
∴ Speed of boat in downstream = x + 5
Distance = 12 km
∴ Time taken in downstream = 12/(x + 5) --- ( ii )
According to question
Time taken in upstream = time taken in downstream
∴ Eq ( i ) = Eq ( ii )
8 ( x + 5) = 12 ( x - 5 )
8x + 40 = 12x - 60
4x = 100
x = 25
∴ Speed of boat in still water is 25km/h
Answered by
12
let the speed of boat in still water be 'x' km/ hr
speed of stream = 5km/ hr
speed = distance/ time
speed upstream
(x - 5) km/ hr = 8/ t
t = 8 /( x - 5) --(1)
speed downstream
(x + 5) km/ hr = 12/ t
t = 12/ ( x + 5) --(1)
since, the time taken is same .
so then from(1) and (2)
8/( x - 5) = 12/ (x + 5)
8( x + 5) = 12(x - 5)
8x + 40 = 12x - 60
4x = 100 => x = 25 km/hr
Answer:
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speed of boat in still water = 25km/hr
speed of stream = 5km/ hr
speed = distance/ time
speed upstream
(x - 5) km/ hr = 8/ t
t = 8 /( x - 5) --(1)
speed downstream
(x + 5) km/ hr = 12/ t
t = 12/ ( x + 5) --(1)
since, the time taken is same .
so then from(1) and (2)
8/( x - 5) = 12/ (x + 5)
8( x + 5) = 12(x - 5)
8x + 40 = 12x - 60
4x = 100 => x = 25 km/hr
Answer:
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speed of boat in still water = 25km/hr
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