Between which pair of ports does the Panama Canal shorten the sea route by the greatest distance?

Introduction / Context:
This question tests knowledge of world geography and major shipping routes. The Panama Canal is one of the most important man made waterways because it allows ships to pass between the Atlantic and Pacific Oceans without going all the way around South America. The question specifically asks between which pair of ports the canal shortens the distance by the largest amount, which requires comparing great circle routes and canal routes.

Given Data / Assumptions:

• The geographic feature is the Panama Canal linking the Atlantic and Pacific Oceans through Central America.
• We want the pair of ports for which the canal gives the maximum saving in distance.
• The options include port pairs involving Liverpool, Shanghai, Sydney, New York, Honolulu, San Francisco and London.
• We assume standard sea routes that would otherwise go around Cape Horn or through other long paths if the canal did not exist.

Concept / Approach:
Before the canal was built, ships traveling between the east coast and west coast of North America had to go around Cape Horn at the southern tip of South America. This path is extremely long. The Panama Canal cuts across the narrow Isthmus of Panama and reduces the distance between east coast ports like New York and west coast ports like San Francisco by many thousands of kilometers. Routes from Europe to Asia also benefit, but the relative saving is still largest between ports on opposite coasts of the same continent.

Step-by-Step Solution:
Step 1: Consider the route from New York to San Francisco without the canal. The ship must go down the Atlantic, around Cape Horn and then up the Pacific coast, which is a very long path.Step 2: With the Panama Canal, the ship can cross Central America through the canal and avoid the long detour around South America, saving a very large distance.Step 3: For routes like Liverpool to Shanghai or Liverpool to Sydney, alternative routes already exist around the Cape of Good Hope or through the Suez Canal, so the relative distance saving from Panama is smaller.Step 4: The route New York to Honolulu is partly across the Pacific and does not depend as strongly on the canal for huge savings.Step 5: Comparing all options, the maximum distance saved by using Panama Canal is for New York to San Francisco.

Verification / Alternative check:
Textbooks and atlases that discuss the Panama Canal often highlight how it transformed trade between the east and west coasts of the United States. They show examples of route maps where the distance between New York and San Francisco is reduced dramatically. While European Asian routes also benefit, the classic example of maximum shortening always involves the two coasts of North America. This confirms that New York and San Francisco is the correct pair.

Why Other Options Are Wrong:
Liverpool and Shanghai can use routes via the Suez Canal and the Indian Ocean, so the Panama Canal is not the most direct or most beneficial choice. New York and Honolulu mainly involve travel across the Pacific Ocean, so the canal does not play the same central role. Liverpool and Sydney can be linked via the Cape route, and London and Tokyo also find more efficient paths using other canals or capes. None of these pairs show as dramatic a saving as New York to San Francisco.

Common Pitfalls:
Candidates sometimes focus on very long intercontinental routes and forget that the question asks for maximum shortening, not simply long journeys. Another mistake is to ignore the existence of the Suez Canal and think that all European Asian trade must use Panama. Remember that Panama is especially important for links between the Atlantic and Pacific coasts of the Americas, whereas Suez is more important for Europe Asia traffic.

Final Answer:
The Panama Canal shortens the sea route the most between New York and San Francisco.