The Yankee Clipper leaves the pier at 9:00 am at 8 knots. A half hour later the River Rover leaves the same peir going in the same direction traveling at 10 knots. At what time will the River Rover overtake the Yankee Clipper?
Please help me solve this using the d=rt formula and write an equation.
Arithmetic:
Clipper's lead = 8 knots * (1/2) hour = 4 nautical miles
For each hour, the Rover catches up by (10-8)=2 nautical miles.
Time required to catch up = 4/2 hours (after 9:30)
Time the Rover will catch up = 11:30
Algebra:
Let t=time (as of 9:30) to catch up
10*t - 8*t = 8*(1/2)
2t = 4
t=2
The Rover will catch up at 11:30.
To solve this problem using the d=rt formula, we need to set up an equation that represents the distance traveled by each boat over time.
Let's denote the time it takes for the River Rover to overtake the Yankee Clipper as "t" in hours. Since the Yankee Clipper departed at 9:00 am and the River Rover set off half an hour later, the River Rover had a head start of 0.5 hours.
The equation for the distance traveled by the Yankee Clipper is: d1 = r1 * (t + 0.5). Here, r1 represents the speed of the Yankee Clipper in knots, which is 8 knots, and (t + 0.5) represents the time it takes for the Yankee Clipper to be overtaken by the River Rover.
The equation for the distance traveled by the River Rover is: d2 = r2 * t. Here, r2 represents the speed of the River Rover in knots, which is 10 knots.
Since both boats will eventually meet when the River Rover overtakes the Yankee Clipper, the distances d1 and d2 are equal. Therefore, we can set up the equation:
r1 * (t + 0.5) = r2 * t
Plugging in the given values for r1 and r2, we get:
8 * (t + 0.5) = 10 * t
To solve for t, we can distribute 8 to t and 0.5:
8t + 4 = 10t
Rearranging the equation to isolate t:
10t - 8t = 4
2t = 4
t = 4 / 2
t = 2
So, the River Rover will overtake the Yankee Clipper after 2 hours.
To find the time when the River Rover will overtake the Yankee Clipper, we add this 2 hours to the River Rover's departure time of 9:30 am.
9:30 am + 2 hours = 11:30 am
Therefore, the River Rover will overtake the Yankee Clipper at 11:30 am.