Competition problem — Combinatorics

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Combinatorics Difficulty 5.0 AIME, harder Find the answer

4. A tourist starts rowing from the pier at 10:15 and wishes to return no later than 13:00. It is known that the river current speed is 1.4 kilometers/hour, and the boat's speed in still water is 3 kilometers/hour. If he rests for 15 minutes after every 30 minutes of rowing, without changing direction, and can only turn back after a rest, how far can he row from the pier at most?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Add the last 30 minutes of shrimp molting to the cycle.
$\frac{1}{2}(3+1.4) \div \frac{1}{4} \times 1.4=2.55 \text { (gong yao). }$

It is known that returning in time is not possible. Therefore, the only option is to paddle out, and in three weeks the farthest distance that can be reached is
$2 \times 0.45+\frac{1}{2}(3-1.4)=1.7 \text { (gong: }$

However, it is still possible to return in time,

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.