A girl starting at 11 A.M., travels east at 4 km/hr while a boy, starting at noon from the same point, travels north at 6 km/hr. How fast are they separating at 3 P.M.

Q: Two cars start moving from the same point. One travels south at 48 mi/h and the other travels west…

A: Given  Speed of first car =48 mi/h towards south Speed of second car =20 mi/h towards west

Q: A red truck moving 100 km/h overtakes a 1.5 km long train moving in the same direction on a track…

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Q: Two small planes approach an airport, one flying due west at 120 mi/hr and the other flying due…

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Q: A rocket, rising vertically, is tracked by a radar station that is on the ground 5 mi from the…

A: Given that: Rate of increase of distance from radar station = 2000 mi/hDistance between radar…

Q: A 16-foot long Ford Fusion wants to pass a 50-foot truck traveling at 55 mi/h. How fast must the car…

A: The length of Ford Fusion is 16 foot The length of the truck is 50 foot To pass the truck…

Q: Car A leaves a parking lot at 9 am and travels eastward at the rate of 60 kph. Another vehicle, car…

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Q: An airliner passes over an airport at noon traveling 520 mi/hr due east. At 1:00 p.m., another…

A: Given: An airliner passes over an airport at noon traveling 520 mi/hr due east. At 1:00 p.m.,…

Q: A rabbit is traveling at a pace of 250 meters per hour. How fast is the rabbit  traveling in…

A: Given:    Distance = 250 meter per hour

Q: At noon, ship A is 150 km west of ship B. Ship A is sailing east at 30 km/h and ship B is sailing…

A:

Q: A kite is 40 ft. high with 50 ft. of cord out. If the kite moves horizontally at 5 mi. per hr.…

A: Draw the position of kite as shown below.

Q: The current in a typical Mississippi River shipping route flows at a rate of 4 mph. In order for a…

A: Let the speed of barge in still water be x miles per hour. Given the speed of river is 4 miles per…

Q: An airliner passes over an airport at noon traveling 510 mi / hr due east. At 1:00 p.m., another…

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Q: A 5 foot girl is walking toward a 20- foot lamppost at the rate of 6 feet per second. How fast is…

A:

Q: A plane is flying at a constant altitude of 1 mile and a speed of 400 mph toward an observer on the…

A: The plane is flying at a constant altitude of 1 mile. Let x be the horizontal distance and y be the…

Q: A 13-foot ladder is placed against a wall. If the top of the ladder is sliding down the wall at 3…

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Q: 4. Shirogane, who is 175 cm tall, is walking at a rate of 3 meters per second towards a lamppost…

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Q: At noon, ship A is 100 km west of ship B. Ship A is sailing south at 25 km/h and ship B is sailing…

A: The below diagram represents the pictorial representation of the given problem.The position of the…

Q: Two cars that started at the same point are driving away from each other. The first car is driving…

A: Given,          Two cars that started at the same point are driving away from each other. The first…

Q: Car A is traveling west at 50 mi/h and Car B is traveling north at 60 mi/h. Both are headed for the…

A: In first question we find out dz/dt .and in 2nd question first we put dy/dx=0 for extreme values.and…

Q: The volume of a cube is increasing at a rate of 60 in/sec. At what rate is the length of each edge…

A: The objective is to find the rate at which the length of each edge of the cube is changing when the…

Q: A car traveling at 45 miles per hour is brought to a stop, at constant deceleration, 132 feet from…

A: Given: A car traveling at 45 miles per hour.

Q: The White River flows at a rate of 4 km/h. In order for a boat to travel 76.8 km upriver and then…

A: Let x be the speed of water still in water. Then, Upstream speed is x-4 and downstream speed is x+4.…

Q: At noon, ship A is sailing north at a speed of 7mph, at the same time ship B, 5 miles west of ship…

A: Given, at noon, Ship A is sailing north at a speed of 7mph. At the same time, Ship B, which is 5…

Q: Shan, who is 2 meters tall, is approaching a post that holds a lamp 6 meters above the ground. If he…

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Q: At noon, ship A is 170 km west of ship B. Ship A is sailing east at 40 km/h and ship B is sailing…

A:

Q: The top of a 22 foot ladder, leaning against a vertical wall, is slipping down the wall at the rate…

A:

Q: Two boats leave a dock at the same time. One boat travels south at 30 mi>hr and the other travels…

A: Find the rate of change the distance between the boats.

Q: A train, starting at noon, travels north at 40 ml per hr. Another train, starting from the same…

A:

Q: A man 6 ft tall walks along a level sidewalk away from a lamppost. On the post is a street light 18…

A:

Q: The sides of a cube are increasing at a rate of 1cm/s. How fast is the diagonal of the cube changing…

A: Explanation: Given that,  The sides of a cube are increasing at a rate of 1cm/s. The objective is to…

Q: A boat leaves a dock at 4:00 PM and travels due south at a speed of 20 km/h. Another boat has been…

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Q: A van is 5km due north of a bus at 2:00PM. If the van is traveling northward at the rate of 60 kph…

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Q: Two automobiles start from a point A at the same time. One travels west at 80 km/hr and the other…

A: Topic:- application of derivatives

Q: Car A is traveling west at 50 mi/h and car B is traveling north at 60 mi/h. Both are headed for the…

A: topic - application of derivatives

Q: Two small planes approach an airport, one flying due west at 100 mi/hr and the other flying due…

A: Solution is here

Q: Two cyclists, 90 mi apart, start riding toward each other at the same time. One cycles twice as fast…

A: Given that, the distance between two cyclists is 90 mi, and one cycles twice as fast as the other…

Q: 2. A motorist travels for 20km at one speed, and then increased her speed by 20 kph for next 30 km.…

A:

Q: Two cars are initially 1200 miles apart. At the same time Car A starts driving at 35 mph to the east…

A: Given ,  Two cars are initially 1200 miles apart  At the same time Car A starts driving at 35 mph to…

Q: Two cars start moving from the same point. One travels south at 84 mi/h and the other travels west…

A:

Q: At noon,ship a is 130 km west of ship b.Ship a is sailing east at 25 km/h and ship b is sailing…

A:

Q: At noon, ship A is 170 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing…

A:

Q: A 30-foot ladder is leaned up against a 2-story building with 8-foot floors. The bottom of the…

A: Consider the diagram below with marked information: Speed of change in base is 6 feet per second.

Q: A computerized spin balance machine rotates a 25-inch-diameter tire at 480 revolutions per minute.…

A:

Q: A kite flying 80m high is blown horizontally by the wind at a velocity of 5m/s. If the string is…

A: We are given that a kite flying at 80m height is blown horizontally by the wind at a velocity of…

Q: The top of a 18 foot ladder, leaning against a vertical wall, is slipping down the wall at the rate…

A:

Q: Two cars start moving from the same point. One travels south at 64 mi/h and the other travels west…

A:

Q: 6. Shan, who is 2 meters tall, is approaching a post that holds a lamp 6 meters above the ground. If…

A:

Q: A man, running 3 meters per second in an open field, runs east for 30 seconds, then turns north.  If…

A: Since the man ran 3m/s east for 90 sec so he is 90 m from the searchlight. Consider the diagram…

Q: At noon, ship A is 180 km west of ship B. Ship A is sailing east at 40 km/h and ship B is sailing…

A: Consider the following: