SOLUTION: A small boat sends a distress signal giving its location as 10 miles from shore in choppy seas and says it is making only 5 knots. A Coast Guard boat is dispatched from shore to g

Question 1182752: A small boat sends a distress signal giving its location as 10 miles from shore in choppy seas and says it is making only 5 knots. A Coast Guard boat is dispatched from shore to give aid: it averages 20 knots. How long before it meets the disabled boat if they are traveling toward each other? How far did each travel?

Answer by greenestamps(13211) (Show Source): You can put this solution on YOUR website!

The ratio of the speeds of the two boats is 20:5 = 4:1, so the ratio of distances traveled is 4:1.

If your mental arithmetic is good, you can solve that mentally -- the small boat travels 2 of the 10 miles and the Coast Guard boat travels 8.

Or if you need to use formal algebra, using the ratio 4:1 of the distances traveled by the two boats, the small boat travels x miles and the Coast Guard boat travels 4x miles, and the total distance traveled is 10 miles:
x+4x=10
5x=10
x=2
4x=8

The required time can be determined using the distance and speed of either boat: 2 miles at 5 knots for the small boat or 8 miles at 20 knots for the Coast Guard boat.

Of course you need to deal with the conversion between knots and miles per hour; that part I leave to you.

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