Math, asked by navyamisra, 1 year ago

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 nickkaushiknick
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 )

\frac{8}{x-5}=\frac{12}{x+5}

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 TheLostMonk
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
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