Question

A fishing boat leaves port at 4 miles per hour at a bearing of 80∘ for 3 hours, then turns to a bearing of 0∘ at 3 miles per hour for 4 hours, and finally changes to a bearing of 200∘ at 6 miles per hour for 5 hours. At this point, the boat heads directly back to port at a speed of 2 miles per hour. Find the time it takes the boat to return to port as well as the boat's bearing as it does.

Return time:
hours
Return bearing:

Answer 1

A fishing boat leaves port at 4 KNOTS at a HEADING of 80∘ for 3 hours, then turns to a HEADING of 0∘ at 3 KNOTS for 4 hours, and finally changes to a HEADING of 200∘ at 6 KNOTS for 5 hours. At this point, the boat heads directly back to port at a speed of 2 KNOTS. Find the time it takes the boat to return to port as well as the boat's HEADING as it does.
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note 200 deg is 20 degrees west of south. A knot is a nautical mile/hour

North distance = 12 cos 80 - 30 cos 20 + 12 = -14.1

East distance = 12 sin 80 - 30 sin 20 = 1.55

so we turn for home must go 1.55 miles west and 14.1 miles north

let A = angle west of north
tan A = 1.55/14.1 = .11
A = 6.27 degrees west of north
or heading = 360 -6.27 = 353.7 degrees

distance = 14.1/cos 6.27 = 14.2 miles

Answer 2

Oh the time = 14.2/2 = 7.1 hours

Answer 3

A bearing by the way is the direction of something from you. For example that lighthouse bears 10 degrees off our starboard bow or 27 degrees magnetic. The direction you point the fishing boat is heading.