Hallp quic a tourist sailed against the current on a river for 6 km, and then he sailed in a lake for 15 km. in the lake he sailed for 1 hour longer than he sailed in the river. knowing that the current of the river is 2 km/hour, find the speed of the boat while it is traveling in the lake.

To solve this we are going to use the formula for speed: 
where
is the speed
is the distance 
is the time 

Let  be the speed of the boat in the lake,  the speed of the boat in the river,  the time of the boat in the lake, and  the time of the boat in the river. 

We know for our problem that the current of the river is 2 km/hour, so the speed of the boat in the river will be the speed of the boat in the lake minus 2km/hour:

We also know that in the lake the boat sailed for 1 hour longer than it sailed in the river, so:


Now, we can set up our equations.
Speed of the boat traveling in the river:

But we know that , so:
equation (1)

Speed of the boat traveling in the lake:

But we know that , so:
equation (2)

Solving for  in equation (1):

equation (3)

Solving for  in equation (2):



equation (4)

Replacing equation (4) in equation (3):



Solving for :





or 

We can conclude that the speed of the boat traveling in the lake was either 6 km/hour or 5 km/hour.

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