Two boats...

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Two boats on opposite shores of a river start moving towards each other. When they pass each other they are 700 yards from one shoreline. They each continue to the opposite shore, immediately turn around, and start back. When they meet again they are 300 yards from the other shoreline. Each boat maintains a constant speed throughout.

Now the questions:
1. How wide is the river?
2. What is the speed of each boat?

(An explanation would be nice Very Happy

)

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D = width of river

When they first meet:
first boat goes 700, second boat goes D-700

When they meet the second time:
first boat goes D+300, second boat goes 2D-300

Since their rates are constant the ratios of the distances for the two legs must be equal:
700 / (D+300) = (D-700) / (2D-300)

Simplifying yields:
D^2 - 1800D = 0

D = 0 and D = 1800 are the possible solutions.
Obviously, D can't be 0.

Computing the speeds is trivial once the width of the river is known.

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Actually computing the speed is impossible, but you know that the faster boat travels at 1.57 times the speed of the slower.

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You're right - not times were mentioned. Embarrassed

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markr wrote:

You're right - not times were mentioned.

No times

I just used a ratio to represent it :wink:

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Two boats...

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