A ship leaves a port at 12:00 Noon and sails East at speed of 10 miles/hour. Another ship leaves
the same port at 1:00 PM and sails North at a speed of 20 miles/hour. At what time are the two
ships going to be 50 miles apart from each other? (Hint: Distance = Speed * Time)
To find out at what time the two ships are 50 miles apart from each other, we need to determine how long it will take for the two ships to reach a distance of 50 miles.
Let's consider the first ship that leaves the port at 12:00 Noon and sails East at a speed of 10 miles/hour.
From 12:00 Noon till 1:00 PM (1 hour), this ship would have covered a distance of 10 miles (Speed * Time = 10 miles/hour * 1 hour = 10 miles).
Now, let's consider the second ship that leaves the port at 1:00 PM and sails North at a speed of 20 miles/hour.
Since the first ship sailed for 1 hour and covered a distance of 10 miles, the two ships are already 10 miles apart when the second ship starts sailing.
Now, we need to find the additional distance the two ships need to cover to be 50 miles apart. We can use the concept of Pythagoras theorem to calculate the distance between the two ships.
The horizontal distance traveled by the first ship is 10 miles (since it has been sailing for 1 hour at a speed of 10 miles/hour).
The vertical distance traveled by the second ship is also 10 miles (since it starts sailing 1 hour later, and also at a speed of 20 miles/hour for that hour).
Using the Pythagoras theorem, we can calculate the distance between the two ships:
Distance = √(horizontal distance^2 + vertical distance^2)
Distance = √(10^2 + 10^2)
Distance = √(100 + 100)
Distance = √200
Distance = 14.14 miles (approximately)
So, to be 50 miles apart, the two ships need to cover an additional distance of 50 - 14.14 = 35.86 miles.
Now, we can use the formula Distance = Speed * Time to find the time it takes for the ships to cover this additional distance of 35.86 miles.
Time = Distance / Speed
Time = 35.86 miles / 20 miles/hour
Time = 1.793 hours (approximately)
Therefore, it will take approximately 1.793 hours for the two ships to be 50 miles apart from each other.
To find the time at which they will be 50 miles apart, we need to add this additional time to the time when the second ship started sailing.
1:00 PM + 1.793 hours = 2.793 hours
Hence, the two ships will be approximately 50 miles apart from each other at around 2:48 PM.