A motorboat covers a certain distance downstream, in a river in 3 hours. It covers the same distance upstream in 3 hours and a half. If the speed of water is , then the speed of the boat in still water is:

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answer is B.

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Detailed Solution

Concept- First, we'll make an assumption about a variable affecting the boat's speed and the distance it travels. As we move downstream, the river's speed increases with the speed of the boat, and as we move upstream, the speed of the water decreases with the speed of the boat. To create equations that can be solved for the values of speed and distance, we will apply the speed formula from physics. The speed equation is s.

, where

is the speed, I is the distance it covers and

is the time required to cover the distance of I at speeds.
Let the speed of the boat be x and the distance it covers be I.
It is given to us that when moving downstream, it takes 3 hours.
Therefore,

hours. The net speed downstream will be the sum of the speed of the boat and the speed of the river.
Thus, net speed downstream

So, we will use the equation of speed.

Now, when the boat is going upstream, it takes 3.5 hours.
Therefore,

hours. The net speed upstream will be the sum of the speed of the boat and the speed of the river.
Thus, net speed upstream

So, we will use the equation of speed.
Thus, net speed upstream

So, we will use the equation of speed.

Now, we shall solve (1) and (2).
Subtract (2) from (1).

Thus, the speed of the boat

.
Hence, option (2) is the correct option.

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