A boat heads south at 120 mph while a steamer heads east at 50 mph. If they started from the same dock and at the same time, when will the distance between them be 130 mi?

Question

Mathematics

Sebastian Pollard

26 November, 01:46

A boat heads south at 120 mph while a steamer heads east at 50 mph. If they started from the same dock and at the same time, when will the distance between them be 130 mi?

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Answers (1)

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Davin Monroe · Answer 1

1 hour after they leave

Step-by-step explanation:

The distance each travels is proportional to its speed. The given speeds are at right angles to each other in a 5:12 ratio. The Pythagorean theorem tells you the hypotenuse of such a right triangle will have length ...

√ (5²+12²) = √169 = 13

That is the speeds are in the ratio 5:12:13, where 13 represents the relative separation speed. Actual speeds are then 50 mph : 120 mph : 130 mph.

So the distance between the boat and steamer will be increasing at 130 mph. The distance will be 130 miles after 1 hour.