Andrea, Fred, and Brian leave a dock and sail 10km at a bearing of 090degrees to a fishing spot. After fishing for a while, they sail on a bearing of 210 degrees to another spot 6 km away. The boat travels at 15 km/h. If the time is now 3:30 P.M. how long can they continue to fish at this location if they must return to the dock before dark at 6:30 P.M. Calculate the answer to the nearest minute

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Did you draw a picture? That always helps.

Since they travel 10 km at 90 degrees, it is obvious the coordinates of their first point is (10,0).

Then, they travel at an azimuth of 210 degrees for 6km.

Now, just use sine and cosine to find the coordinates of the next point, A.

x=10+6sin(210), \;\ y=0+6cos(210)

Now, use the distance formula to find how far it is back to the origin, O.

Divide that into their rate to see how long it would take to get back. Then, you can easily find how long they can fish before they start back.