A LIGHTHOUSE IS 10 MILES NORTHEAST OF A DOCK. A SHIP LEAVES THE DOCK AT NOON,AND SAILS EAST AT A SPEED OF 12 MILES AN HOUR. AT WHAT TIME WILL IT BE 8 MILES FROM THE LIGHTHOUSE?

A lighthouse is 15 units of length northwest of a dock. A ship leaves the dock at 8:00 am and travels west at 12 units of length per hour. At what time will the ship be 12 units of length from the lighthouse for the first time?

Well, let's see. If the ship is sailing east from the dock and the lighthouse is to the northeast, it means that the ship will be gradually getting closer to the lighthouse while moving away from the dock.

At a speed of 12 miles an hour, the ship will take 8/12 = 2/3 hours to cover a distance of 8 miles.

Converting this into minutes, we have (2/3) * 60 = 40 minutes. So, it will take the ship 40 minutes to be 8 miles from the lighthouse.

Now, let's factor in the starting time. If the ship leaves the dock at noon and takes 40 minutes to reach the 8-mile mark, we simply add 40 minutes to the time, which gives us 12:40 PM.

Therefore, the ship will be 8 miles from the lighthouse at 12:40 PM. Just make sure the ship brings a camera to capture the beautiful view!

To determine at what time the ship will be 8 miles from the lighthouse, we can use the distance formula in the form of a right triangle.

The distance between the lighthouse and the dock is the hypotenuse of the right triangle, and the distance the ship travels is one of the legs.

Given:
- The lighthouse is 10 miles northeast of the dock.
- The ship leaves the dock at noon and sails east at a speed of 12 miles per hour.

Let's break down the problem step-by-step:

Step 1: Determine the distance the ship has traveled.

To find the distance the ship has traveled, we need to calculate the time it takes for the ship to reach a distance of 8 miles from the lighthouse.

Distance = speed x time.

The ship is traveling at a speed of 12 miles per hour.

Let's denote the time it takes to reach a distance of 8 miles from the lighthouse as "t".

Distance = speed x time.
8 = 12t

Solving for t:
t = 8/12
t = 2/3

Therefore, it will take the ship 2/3 of an hour to reach a distance of 8 miles from the lighthouse.

Step 2: Calculate the time when the ship will be 8 miles from the lighthouse.

Since the ship leaves the dock at noon and it will take 2/3 of an hour to reach a distance of 8 miles from the lighthouse, we can add 2/3 of an hour to noon.

To add 2/3 of an hour to noon, we need to convert 2/3 of an hour to minutes.

1 hour = 60 minutes

2/3 of an hour = (2/3) x 60 minutes = 40 minutes

Adding 40 minutes to noon:
12:00 PM + 40 minutes = 12:40 PM

Therefore, the ship will be 8 miles from the lighthouse at 12:40 PM.

To solve this problem, we need to use the information provided about the ship's speed and direction. Here's how you can approach it:

1. Start by drawing a diagram. Draw a point representing the dock, another point representing the lighthouse, and a straight line connecting them to indicate the initial distance of 10 miles.

Lighthouse ----------------------------- Dock

2. Since the ship is sailing east, draw an arrow pointing to the right from the dock, indicating the ship's direction of motion.

Ship --->

3. Given that the ship's speed is 12 miles per hour and it leaves the dock at noon, we can use the formula: distance = speed × time.

4. Let's assume the amount of time it takes for the ship to be 8 miles from the lighthouse is "t" hours.

5. The distance between the ship and the lighthouse can be calculated using the Pythagorean theorem: distance^2 = (10)^2 + (8)^2.

Simplifying this equation, we get: distance^2 = 100 + 64 = 164.

6. Now, we can calculate the time it takes for the ship to travel 8 miles from the dock using the speed-distance-time formula: 8 = 12t.

Dividing both sides of the equation by 12, we get: t = 8/12 = 2/3 hours.

7. Convert the time from hours to minutes: 2/3 hour = (2/3) × 60 minutes = 40 minutes.

8. So, the ship will be 8 miles from the lighthouse 40 minutes after it leaves the dock.

9. To determine the time when the ship will be 8 miles away from the lighthouse, we need to add the time it took for the ship to travel 40 minutes to the original departure time of noon.

40 minutes after 12:00 p.m. is 12:40 p.m.

Therefore, the ship will be 8 miles away from the lighthouse at 12:40 p.m.

since the lighthouse is 10 mi NE of the dock, it is 7.07mi east and 7.07 mi north. (legs of a 45-45-90 triangle)

Now, if the ship is 8 mi from the lighthouse, we have a new x-7.07-8 triangle, so x = 3.74.

Now, the distance from the dock to the ship is 7.07 - 3.74 = 3.33 mi.

At 12 mi/hr, that would take 3.33/12 = .277777 hours, or 16'40"

So, at 12:16:40 the ship is 8 mi from the lighthouse

Note: the ship will also be 8 miles from the lighthouse after it has passed it and is east of the lighthouse. From the above data, you can figure the second time with no trouble.