Question

A boat takes 2.5 hours less to travel 100 km downstream than to travel 75 km upstream. If the speed of the current is 5 km/hr, find the speed of the boat in still water. ?​

Answer 1

Let the speed of the boat is 'x' km/hr. We have

75/(x-5) - 100(x+5) = 5/2

⇒ 25(3(x+5) - 4(x-5) / x2 - 25) = 5/2

⇒ 10(3x+15 - 4x+20) = x2 - 25

⇒ 10(35 - x) = x2 - 25

⇒ 350 - 10x = x2 - 25

⇒ x2 + 25x - 15x - 375 = 0

⇒ x(x+25) - 15(x+25) = 0

⇒ (x+25) (x-15) = 0

⇒ x = 15 km/hr (Rejecting the negative value)

Answer 2

Concept :

An aqueduct is an example of a stream. The boat is said to be upstream if it is flowing in the opposite direction from the stream. In this case, the boat's net speed is called upstream speed. If the boat is flowing along the direction of the stream, it is called downstream.

Given: A boat takes $2.5$hours less to travel $100 km$ downstream than to travel $75 km$ upstream. If the speed of the current is $5 km/hr$.

Find: If the speed of the current is $5 km/hr$, find the speed of the boat in still water.

Solution:

Let the speed of the boat is $'x' km/hr$. We have

$75/(x-5) - 100(x+5) = 5/2$

⇒ $25(3(x+5) - 4(x-5) / x2 - 25) = 5/2$

⇒ $10(3x+15 - 4x+20) = x2 - 25$

⇒ $10(35 - x) = x2 - 25$

⇒ $350 - 10x = x2 - 25$

⇒$x2 + 25x - 15x - 375 = 0$

⇒ $x(x+25) - 15(x+25) = 0$

⇒$(x+25) (x-15) = 0$

⇒ $x$ = $15 km/hr$

Hence the speed of the boat in still water is $15 km/hr$.

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