Question

two cruise ships left Maui traveling in the opposite directions. The one heading east was going 12 mph faster than the one heading west. After six hours, the ships were 300 miles apart. How fast did the ship going east travel?

Answer 1

To find the speed of the eastbound ship, set up an equation considering both ships' speeds and distances traveled over six hours. The eastern ship's speed is determined to be 33 mph after solving the equation.

Step-by-step explanation:

The problem involves determining the speed of a cruise ship heading east based on the information provided about two ships traveling in opposite directions. According to the question, the eastern ship travels 12 mph faster than the western ship, and after six hours, the ships are 300 miles apart. We can solve this by setting up an equation where the sum of their distances after six hours equals 300 miles.

Step-by-step solution:

1. Let the speed of the western ship be x mph.
2. Then, the speed of the eastern ship is x + 12 mph.
3. The distance the western ship travels in 6 hours is 6x miles.
4. The distance the eastern ship travels in 6 hours is 6(x + 12) miles.
5. The total distance apart is the sum of their distances: 6x + 6(x + 12) = 300.
6. Solving the equation, we find that x = 21 mph.
7. Therefore, the speed of the eastern ship is 21 + 12 = 33 mph.

The eastern ship's speed is 33 mph.

Answer 2

Answer: We can start solving this problem by using the information given: the ships are traveling in opposite directions and the speed difference between them is 12 mph. Let's call the speed of the ship heading east x and the speed of the ship heading west x-12.

We also know that the ships were 300 miles apart after 6 hours. The distance between the two ships can be represented as the sum of the distances traveled by each ship, which is x*6 + (x-12)*6 = 300.

We can use this equation to find the value of x.

x*6 + (x-12)*6 = 300

We can simplify it as:

x6 + x6 - 72 = 300

x12 - 72 = 300

x12 = 372

x = 31

So the ship heading east travels at 31 mph.

It is important to notice that the ship going west was 12 mph slower than the ship going east, so the speed of the ship going west is 31-12 = 19 mph.

It is also important to notice that the speed of each ship, x and x-12, are in the same units (mph) and also the distance, 300 miles, and the time, 6 hours, are also in the same units (hours and miles)

Step-by-step explanation: