Question

Roger Waters can scrape up just enough money to rent a canoe for 1 hour and 30 minutes. If he paddles out on a lake at 4 kph and returns at 2 kph, how far will he have paddled the canoe?

Which of the following is a true statement based on this problem?

Answer 1

The distance paddling out on a lake is 2 kilometres and the distance returning back is also 2 kilometres. In total, 4 kilometres.

Explanation:

Let t hours be the time it takes Roger to puddle out on a lake. Then
`\left(1(1)/(2)-t\right)` hours is the time it takes him to return (note that 1 hour and 30 minutes is exactly
`1(1)/(2)` hours).

1. If he paddles out on a lake at 4 kph for t minutes, then the distance is

`4\cdot t=4t\ km.`

2. If he returns at 2 kph, then the distance is

`2\cdot \left(1(1)/(2)-t\right)=3-2t\ km.`

3. These distances are the same, thus

`4t=3-2t,\\ \\6t=3,\\ \\t=(1)/(2)\ hour.`

The distance paddling out on a lake is 2 kilometres and the distance returning back is also 2 kilometres. In total, 4 kilometres.