A 30-foot ladder is leaned up against a 2-story building with 8-foot floors. The bottom of the ladder begins to slide away from the building at a rate of 6 feet per second. How fast is the ladder sliding down the building as its top passes the ceiling of the 1st floor?

Q: A streetlight is mounted at the top of a 16 foot pole. An 8 foot tall Sasquatch walks away from the…

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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: 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: A rectangular parallelepiped with an altitude of 10cm has its width decreasing by 2 cm/min and…

A: A rectangular parallelepiped with an altitude of 10cm has its width decreasing by 2 cm/min and…

Q: A child who is 4 feet tall walks at a speed of 3 feet per second away from a lamp post that is 20…

A: Given that the child is 4 feet tall and he walks at speed of 3 feet per second from lamp post of 20…

Q: A person running at 45 kilometers per hour (KPH) is riding a train at 120 KPH going to Manila. Who…

A: Given that , Speed of a person = 45KPH  Speed of a train = 120KPH  Because, we have same unit of…

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

A:

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: The top of a ladder 30 meters long leans against a vertical wall, and the lower end rests on a level…

A: Let the height of wall corresponding to the ladder lean at any instant be denoted as h. Let the…

Q: A 4.5 ft tall man is walking away from a 25 ft tall lamp post.  If he is walking at a rate of 2…

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Q: A weight is attached to one end of a 33-foot rope which passes over a pulley 18 feet above the…

A: The above problem statement can be pictorially represented as:

Q: A 25-foot ladder is leaning against a wall and the base begins to fall away from the wall. When the…

A: A 25-foot ladder is leaning against a wall and the base begins to fall away from the wall. When the…

Q: It takes an ant farm 3 days to consume of an apple. At that rate, in how many days will the ant farm…

A: An ant farm takes 3 days to consume ½ of an apple. → An ant farm consume ½ of an apple in 3 days

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: A 17 feet ladder is leaning against a wall. if the bottom of the ladder is pulled along the ground…

A: Given:- A 17 feet ladder is leaning against a wall. if the bottom of the ladder is pulled along the…

Q: A man 6 feet tall walks at a rate of 5 feet per second away from the light that is 15 feet above the…

A: Consider the given:

Q: A light hangs 15 feet directly above a straight walk on which a man 6 feet tall is walking. How fast…

A:

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

A:

Q: A spotlight on the ground shines on a wall of a building 20 feet away. If a man 6ft tall walks from…

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Q: Suppose a car is going 31 miles per hour and slams on the break and decelerates at 13 feet per…

A:

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

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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 ship has wrecked and its crew of 300 men has been left stranded on a dessert island. The food will…

A: In equation we are equating two sides left hand side and right hand side. It contains variable,…

Q: A 3-m long steel pipe has its upper end leaning against a vertical wall and the  lower end on a…

A: Given that: Length of steel pipe=3mLower end moves away from the wall at a speed = 2cm/s

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

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Q: A man 2m tall is walking at the rate of 2m/s away from a lamp post 7m high. At what rate is the tip…

A:

Q: A van starts off 152 miles directly north from the city of Springfield. It travels due east at a…

A: The distance between the van and the city of Springfield is 152 miles in the north direction. The…

Q: A 10-meter ladder is leaning against the wall of a building. It begins to slide down the wall. When…

A: Let l denote the length of the ladder leaning against the wall of a building Let x denote the…

Q: Each side of a square is increasing at a rate of 6 cm/s. At what rate is the area of the square…

A: Each side of a square is increasing at a rate of 6 cm/s. To determine the rate at which the area of…

Q: A worker uses 450 inches of steel wire to make 300 springs of the same size. At this rate how many…

A: Let he needs ' x ' inches for making 1 spring.

Q: One end of a ladder 25 feet long slides down a vertical wall while the other end moves away from the…

A:

Q: Each side of a square is increasing at a rate of 6 cm/s. At what rate is the area of the square…

A: Given,                     Each side of a square is increasing at a rate of 6 cm/s. The area of the…

Q: A ladder 20 feet long rests against a vertical wall. If the bottom of the ladder slides away from…

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: A 6 foot tall man walks away at the rate of 4 feet per second from the base of the street light 12…

A: Let s be the length of the base of the street light to the shadow, x be the length of the base of…

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: A man 6 feet tall walks at a rate of 2 feet per second away from a light pole that is 16 feet high.…

A: From the figure substitute value of BE, AE, AD and AC in equation (1)

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

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: A kite travels upwards at 30 mph, while a kid runs away at 6mph. What rate is the distance between…

A:

Q: Two cars start moving from the same point. One travels south at 56 mi/h and the other travels west…

A:

Q: A life raft, set adrift from a sinking ship 150 miles offshore, travels directly toward a Coast…

A: Time , distance and speed is related using a formula time=distancespeed .At the same time , both the…

Q: A ladder 25 feet long is leaning against a vertical wall. If the bottom of the ladder is pulled…

A: A ladder 25 feet long is leaning against a vertical wall. The bottom of the ladder is pulled…

Q: A 80 foot ladder leaning against a wall is being pushed so that the bottom of the ladder is sliding…

A: Here dydt=6feet/secondx=48 feety=64feet

Q: One end of a ladder 34 feet long slides down a vertical wall while the other end moves away from the…

A: Note:  According to our guidelines we are supposed to do only first question. Kindly repost other…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.