The amount of oil used by a ship traveling at a uniform speed varies jointly with the distance and the square of the speed. The ship uses 30 barrels of oil in traveling 85 miles at 42 mi/h. How many barrels of oil are used when the ship travels 26 miles at 54 mi/h? Round your answer to the nearest tenth of a barrel, if necessary.
(1 point)
Responses
a 2.3 barrels
b 15.2 barrels
c 49.6 barrels
d 9.2 barrels
d) 9.2 barrels
Explanation:
Let x be the amount of oil used.
Given that the amount of oil used varies jointly with the distance and the square of the speed, we can write the equation as:
x = k * d * s^2,
where x is the amount of oil used, d is the distance traveled, s is the speed, and k is a constant.
From the information given, when the ship travels 85 miles at 42 mi/h, the ship uses 30 barrels of oil. So we have:
30 = k * 85 * 42^2.
Solving for k, we get k = 30 / (85 * 42^2).
Now, we can use this value of k to find the amount of oil used when the ship travels 26 miles at 54 mi/h:
x = k * 26 * 54^2.
Substitute the value of k and solve for x to get:
x = 9.2 barrels.
Therefore, the amount of oil used when the ship travels 26 miles at 54 mi/h is 9.2 barrels.