Question

A river flowing southward has a current of 4 miles per hour. A motorboat in still water maintains a speed of 15 miles per hour. The motorboat starts at the west shore on a bearing of N ​40° E. What is the actual speed and direction of the​ boat

The actual speed of the boat is approximately
miles per hour

The actual bearing of the boat is north blank degrees east

Answer 1

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Answer 2

Answer: x > 0, x = 12 miles per hour

Step-by-step explanation:Let x = speed of boat in still water

Speed upstream (against current) = x-4

Speed downstream (with current) = x+4

Distance = (Rate)(Time), so Time = Distance/Rate

Time upstream + Time downstream = 3

16/(x-4) + 16/(x+4) = 3

16(x+4) + 16(x-4) = 3(x+4)(x-4)

32x = 3(x2 - 16)

3x2 - 32x - 48 = 0

(3x + 4)(x - 12) = 0

x = -4/3 or x = 12

Since x > 0, x = 12 miles per hour