What is the length of YZ?
1 answer:
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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 <span>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:
</span>
We also know that in the lake the boat<span> sailed for 1 hour longer than it sailed in the river, so:
</span>
<span>
Now, we can set up our equations.
Speed of the boat traveling in the river:
</span>
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.
where
Let
We know for our problem that <span>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:
</span>
We also know that in the lake the boat<span> sailed for 1 hour longer than it sailed in the river, so:
</span>
<span>
Now, we can set up our equations.
Speed of the boat traveling in the river:
</span>
But we know that
Speed of the boat traveling in the lake:
But we know that
Solving for
Solving for
Replacing equation (4) in equation (3):
Solving for
We can conclude that the speed of the boat traveling in the lake was either 6 km/hour or 5 km/hour.