The Yankee Clipper leaves the pier at 9:00 am at 8 knots. A half hour later, The River Rover leaves the same pier in the same direction traveling 10 knots. At what time will the River Rover overtake The Yankee Clipper?
To find out when the River Rover will overtake the Yankee Clipper, we need to determine the time difference it will take for the River Rover to catch up with the Yankee Clipper.
Let's assume that the time it takes for the River Rover to overtake the Yankee Clipper is "t" hours.
In the half hour since the Yankee Clipper set sail, it will have traveled a distance of (8 knots * 0.5 hour) = 4 nautical miles.
Now, since the River Rover is traveling at a faster speed of 10 knots, it will be gaining on the Yankee Clipper at a speed difference of (10 knots - 8 knots) = 2 knots.
To calculate the time it takes for the River Rover to catch up with the Yankee Clipper, we can use the formula:
Distance = Speed * Time
The distance traveled by the River Rover is the same as the distance already covered by the Yankee Clipper plus the distance it still needs to catch up, which is 4 nautical miles less than the distance covered by the Yankee Clipper.
So, for the River Rover, the distance traveled is (8 knots * t) + 4 nautical miles.
For the Yankee Clipper, the distance traveled is 8 knots * t.
Setting these distances equal to each other, we can solve for t:
(8 knots * t) + 4 nautical miles = 10 knots * t
Simplifying the equation, we get:
4 nautical miles = 2 knots * t
Dividing both sides by 2 knots, we have:
t = 4 nautical miles / 2 knots
t = 2 hours
Therefore, it will take 2 hours for the River Rover to overtake the Yankee Clipper.
Since the Yankee Clipper left at 9:00 am, it will be caught up by the River Rover at (9:00 am + 2 hours) = 11:00 am.
So, the River Rover will overtake the Yankee Clipper at 11:00 am.