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?

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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?

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Answer 1 · 2017-01-15T02:59:28

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 $2 \times 18 = 36 k m$ $2xx18=36 km$ upstream.

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

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

$\frac{4}{3.2} \times 36 k m = 45 k m$ $4/3.2xx36km=45km$

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

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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?

1 Answer

Explanation:

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