Answer:
The distance paddling out on a lake is 2 kilometres and the distance returning back is also 2 kilometres. In total, 4 kilometres.
Step-by-step explanation:
Let t hours be the time it takes Roger to puddle out on a lake. Then [tex]\left(1\dfrac{1}{2}-t\right)[/tex] hours is the time it takes him to return (note that 1 hour and 30 minutes is exactly [tex]1\dfrac{1}{2}[/tex] hours).
1. If he paddles out on a lake at 4 kph for t minutes, then the distance is
[tex]4\cdot t=4t\ km.[/tex]
2. If he returns at 2 kph, then the distance is
[tex]2\cdot \left(1\dfrac{1}{2}-t\right)=3-2t\ km.[/tex]
3. These distances are the same, thus
[tex]4t=3-2t,\\ \\6t=3,\\ \\t=\dfrac{1}{2}\ hour.[/tex]
The distance paddling out on a lake is 2 kilometres and the distance returning back is also 2 kilometres. In total, 4 kilometres.
