A cruise ship maintains a speed of 15 knots ​(nautical miles per​ hour) sailing from San Juan to​ Barbados, a distance of 600 nautical miles. To avoid a tropical​ storm, the captain heads out of San Juan at a direction of 31° off a direct heading to Barbados. The captain maintains the 15-knot speed for 5 ​hours, after which time the path to Barbados becomes clear of storms.
​(a) Through what angle should the captain turn to head directly to​ Barbados?
​(b) Once the turn is​ made, how long will it be before the ship reaches Barbados if the same 15-knot speed is​ maintained?