Question

A boat covers a certain distance downstream in 5 hours and it covers the same distance upstream in 6 hours .

if the speed of the water is 2 km/h . Find the speed of the boat in still water.​

Answer 1

Answer:

Step-by-step explanation:

Let the speed of boat in still water be x km/hr and the distance be y km.

Speed in downstream = (x + 2) km/hr

Speed in upstream = (x − 2) km/hr

According to the question,

$\frac{y}{x+2} = 5$    ( Speed formula ) --------> (1)

$\frac{y}{x-2} = 6$    ( Speed formula ) --------> (2)

On modifying (1) we get, y = 5(x+2) ---------> (3)

On substituting (3) in (2) we get,

$\frac{5(x+2)}{x-2} = 6$

5x + 10 = 6(x - 2)

5x + 10 = 6x - 12

5x - 6x = -12 - 10

-x = -22

∴ x = 22

Hence, the speed of the boat in still water will be 22 km/hr

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Answer 2

Answer :
Sol:
distance = speed * time
Let’s assume speed of the boat is X
Downstream = speed of the boat + speed of the water so , X + 2
Upstream = speed of the boat - speed of the water so , X -2
Here both distance are common so we form a equation :
X + 2 * 5 = distance -1
X - 2 * 6 = distance -2
We can equate both the equation now
X + 2* 5 = X - 2* 6
X + 10 = X - 12
Speed or the boat = 22 kmph

Shortcut :
Upstream = X
Downstream = Y
Speed of the water = Z
X= 6, Y = 5, Z = 2
Speed of the boat = Z(X+Y) (X-Y)
= 2(6+5) (6-5)
= 2(11) (1)
=22 kmph