You have steamed 520 miles at 22 knots and burning 319 barrels of fuel per day. You must decrease your consumption to 137 barrels per day with 410 miles left in your voyage. What must you reduce your speed (kts) to in order to burn this amount of fuel?
• Fuel consumption vs. time vs. speed – how daily burn relates to hours run and speed • Using proportions to relate old condition (319 bbl/day at 22 kts) to new condition (137 bbl/day at unknown speed) • Converting days to hours and relating barrels per day to barrels per hour
• First, find how many hours per day you are steaming at the original condition, and how many barrels you burn per hour at 22 knots. What is your fuel rate in barrels per hour? • Next, think about what has to stay the same and what has to change: if the fuel burn per hour must go down, how is that linked to speed for this kind of exam problem? • Set up a proportion comparing the original daily burn to the new daily burn and the original speed to the new speed. Which quantities are directly proportional in this simplified scenario?
• Be sure you convert barrels per day to barrels per hour before comparing to speed • Check that your new speed still allows you to cover 410 miles; once you find a candidate speed, compute the time for 410 miles at that speed and confirm the daily burn matches 137 barrels • Verify that your proportion uses the same units on both sides (knots with knots, barrels/day with barrels/day) and that you’re not accidentally mixing miles and hours in the fuel ratio
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