Two ships leave the same island harbor at the same time, and after 4.5 hours they are 270 kilometers apart.
Which statement about the direction and average speed of the two ships could be true?

Explanation

Take each answer choice in turn. For each ship, you first apply the distance formula: \(\text { Rate } \times 4.5=\text { Distance }\). If the ships move in the same direction, you then subtract the shorter distance from the longer one. If the ships move in opposite directions, you then combine the two distances by addition. Only under the scenario in choice (5) are the two ships 270 miles apart after 4.5 hours:
45(4.5) + 15(4.5) = 202.5 + 67.5 = 270
You can rule out the scenario in choice B without applying the Pythagorean Theorem because the combined distance traveled is less than 270 miles. (The combined length of any two sides of a triangle is always greater than the length of the third side.)