The time taken by the two boats to be closest to each other is
Further explanation:
The formula for speed is given as,
Here, represents the speed, represents the distance, and represents time.
The distance between the two points and can be expressed as follows,
The D is distance between the two points.
Given:
A boat leaves a dock at 5:00 pm and travels due south at a speed of 20 km/h. another boat has been heading due east at 15 km/h and reaches the same dock at 6:00 pm.
Calculation:
Consider the dock is at in two dimensions that is .
Boat A is at at 5 P.M. The distance after 5 P.M can be calculated as follows,
The d is the distance and t is the time. -20 represents that the boat is moving in the south direction with speed 20 km/h.
The position of the boat will be .
The boat B was 15 km west of the dock at which means the boat is at at 5 PM.
Boat B is at at 6 P.M. The distance after 6 P.M can be calculated as follows,
The d is the distance and t is the time. 15 represents that the boat is moving in the east direction with speed 15 km/h.
The position of the boat will be .
The distance between the boats can be calculated as follows,
Differentiate the above equation with respect to t.
Now substitute 0 for to obtain the time.
The time in minutes will be .
The time taken by the two boats to be closest to each other is .
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Linear equation
Keywords: Boat, leaves, dock, travels, south, speed, time, heading, east, reaches, 20km/h, two boats, closest, north, west, minutes.