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.

Question

(1 point)
Responses

a 2.3 barrels

b 15.2 barrels

c 49.6 barrels

d 9.2 barrels

Answer 1

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.