Solution to: Rowing Across the River

Call the requested width of the river r.

The first time that Patrick and Eric meet, the total distance that they have traveled together equals the width of the river, or r. The second time that Patrick and Eric meet, the total distance that they have traveled together equals twice the width of the river plus the width of the river, so 3 × r. Because Patrick and Eric row with a constant speed, it also holds that the distance that Patrick traveled in total at the second meeting, equals 3 times the distance that Patrick traveled in total at the first meeting.

The distance that Patrick traveled in total at the first meeting is 180. The distance that Patrick traveled in total at the second meeting is r + 100. When we combine the above, we get the following equation:

3 × 180 = r + 100.

When we solve this equation we find that r = 440.

Therefore, the river is 440 meters wide.

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