Question

A motorboat can travel upstream on a river at 18 km/h and downstream at 30 km/h. How far upstream can the boat travel if it leaves at 8:00 A.M. and must return by noon?

Answer 1

Let's make a first assessment:

Explanation:

The total traveling time is 4 hours. So if it goes upstream for two hours we are sure it will return well within the two hours after that.

In 2 hours it can travel `2xx18=36 km` upstream.

It will then take `36/30=6/5` of an hour to travel back.
This is a total of `2+6/5h=3 1/5 h=3.2h`

But we have a total time of `4h`, so the maximum distance is:

`4/3.2xx36km=45km`

Check the answer:
Upstream: `45//18=2.5h`
Downstream: `45//30=1.5h`
And this adds up to `4h`