SOLUTION: After sailing 16 mi, a sailor changed direction and increased the boat's speed by 3 mph. An additional 12 mi was sailed at the increased speed. The total sailing time was 4 h. Find
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Question 1124970: After sailing 16 mi, a sailor changed direction and increased the boat's speed by 3 mph. An additional 12 mi was sailed at the increased speed. The total sailing time was 4 h. Find the rate of the boat for the first 16 mi. Answer by greenestamps(13209) (Show Source):
The change of direction has nothing to do with the problem; perhaps that was thrown into the statement of the problem to try to confuse you.
The boat travels 16 miles at a speed x and then 12 miles at a speed x+3; the total time is 4 hours.
Use the given distances and speeds for the two parts of the trip to find expressions for the times for the two legs; then write and solve the equation that says the sum of those two times is 4 hours.
If an algebraic solution is not required (as if, for example, this were a problem in a competitive math contest), then at this point you assume the answer is a "nice" number and solve the problem by trial and error -- finding that x=6 is the answer.
But continuing with the formal algebraic solution....
Multiply the whole equation by both denominators to clear fractions:
or
Obviously the negative answer makes no sense in the problem, so the answer is x=6, as we found earlier by trial and error.
ANSWER: The speed of the boat for the first 16 miles was 6mph.
