Two people are walking toward a statue. Alex is 200 m East and walking at a rate of 3 m/s. Charley is 300 m North and is walking at a rate of 4 m/s. At what rate is the distance between Alex and Charley changing?

Q: At 1:00pm, Ship A is 50 miles west of Ship B. Ship A is sailing north at 25 mph and Ship B is…

A: Construct the diagram: The triangles are similar, so  25t20t=x50-xx=2509

Q: Two people start moving from the same point. One heads east, at 24 km/h, the other south at 18 km/h.…

A:

Q: Suppose you drive for 60 miles at 60 miles per hour, then for 60 miles at 30miles per hour. In miles…

A: Recall the equation connecting the three variables of speed, distance and time as: time = distance /…

Q: After 2 hours, the population of a culture of bacteria has increased by 50%. If the rate of growth…

A:

Q: Two cars leave from the same position at the same time. One travels due North at 30 mph, while the…

A:

Q: The quantity of water discharged over a rectangular weir is directly proportional  to the crest…

A:

Q: Two airplanes are flying in the air at the same height: airplane A is flying east at 290 mi h and…

A: Given that:                      Speed of plain A, vA=290 mi/hSpeed of plain B, vB=290 mi/hDistance…

Q: The altitude of a triangle is increasing at a rate of 3 cm/minute while the area of the triangle is…

A:

Q: The altitude of a triangle is increasing at a rate of 1.5 centimeters/minute while the area of the…

A: Let height of triangle = h Base = b Then, we are given that:

Q: Two cars are traveling along perpendicular roads, car A at 40 mph and car B at 60 mph. At noon, when…

A: Related rates is the change of quantity with respect to time t. Find the rate of change of a certain…

Q: A 400-gal tank initially contains 100 gal of brine containing 50 lb of salt. Brine containing 1 lb…

A: Schematic diagram of the given situation:…

Q: Two cars are initially 1000 miles apart on a road that runs East/West. Car A drives 40 miles per…

A: To determine the rate of change of distance between two cars after 10 hours and 20 hours of travel.

Q: a 400 gal tank initially contains 100 gal of brine containing 25 lb of salt. Brine containing 2 lb…

A: A real-life scenario can be described mathematically through a differential equation. By solving the…

Q: At noon, ship A is 12 nautical miles west of ship B. Ship A is sailing south at 15 knots and ship B…

A: v→AB=v→AS+v→SBHere v→AB=velocity of ship A relative to ship Bv→AS=velocity of ship A relative to…

Q: a man 6ft tall walks at rate 5ft/sec away from a lamppost that is 13 ft high. At what rate is the…

A:

Q: An auto A is moving at 20 ft/s and accelerating at 5 ft/s2 to overtake an auto B which is 384 ft…

A:

Q: Two cars, one going east with the speed of 45 mph while the second car heading south at 70 mph, are…

A:

Q: Two people start biking from the same point. One heads east at 13 mph, the other south at 17 mph.…

A: Given, two bikers start at same point. One heading east at 13mph and other heading south at 17 mph.

Q: Two airplanes are flying in the air at the same height: airplane A is flying east at 450 mi/h and…

A: Given Speed of airplane A = 450 mi/h Speed of airplane B = 500 mi/h Distance of airport = 50 miles…

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: Two cars leave from the same position at the same time. One travels due North at 30 mph, while the…

A: Information obtained from question: Let us consider two cars - Car X and Car Y 1. Speed at which car…

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

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

Q: An automobile uses gasoline at a rate of 12 kilometres per litre and has a 65 litre tank. How far…

A:

Q: Two buses are driving along parallel freeways that are 12 miles apart with one bus heading east and…

A:

Q: Two cars are headed for the intersection of the two roads. If Car A is travelling south at 49 km/h…

A:

Q: A 400-gal tank initially contains 100 gal of brine containing 50 lb of salt. Brine containing 1 lb…

A:

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

A:

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…

A:

Q: Mervin and Leela are in bumper cars. They are at opposite ends of a 100-meter track heading toward…

A:

Q: There are 100 bacteria cells in a dish now, but in 5 hours there will be 147 cells. At what rate do…

A: There are 100 bacteria at initial time t=0. In 5 hours that is when t=5, there will be 147 cells. In…

Q: A 450 gal tank initially contains 110 gal of brine containing 52 Ib of salt. Brine containing 1lb of…

A:

Q: A man rows up a stream 4 ½ hours and finds that it requires only 2 ½ hours down the stream. If he…

A: To find: The rate of current. Given: A person rows up a stream 412 hours and 212 hours to down the…

Q: Suppose that two boats leave a dock at different times. One heads due north, the other due east.…

A: Here I am attaching image so that you understand each and every step.

Q: Two buses are driving along parallel freeways that are 4 miles apart with one bus heading east and…

A: We draw the figure as, speed of bus B1 traveling to the east =70 m/h speed of bus B2  travelling…

Q: At what rate is the distance between Jack and Jill changing if Jack is 3 miles from the bakery and…

A: Given:         To determine:

Q: For a car moving at a constant speed the distance traveled varies directly. with the time spent…

A:

Q: Charley stands 34 meters west of Robert. Robert starts walking north at a speed of 2 m/s, and…

A:

Q: Two cars leave from the same position at the same time. One travels due North at 30 mph, while the…

A: distance between cars is charging at a rate of 50 mph detailed solution with explanation is given…

Q: At noon, ship A is 100km100km west of ship B. Ship A is sailing south at 35km/h35km/h and ship B is…

A: Since, ship started at noon or (12:00 pm)Let's assume 't' hours after noon.Ship A is 100km west of…

Q: Ted is driving east at 80 km/hr and Anthony is driving north at 50 km/hr. Both cars are approaching…

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: One car leaves a given point and travels north at 40 mph. Another car leaves 1 HOUR LATER, and…

A: Let's find rate of change distance between the cars changing at the instant the second car has been…

Q: A car travelling north at 60 mph and a truck travelling east at 45 mph leave an intersection at the…

A: It is given that,

Q: A 400-gal tank initially contains 100 gal of brine containing 75 lb of salt. Brine containing 2 Ib…

A: The solution of above question is written below.

Q: Suppose that two boats leave a dock at different times. One heads due north, the other due east.…

A:

Q: At noon, Train A is 20 miles due west of Train B. Train A is moving west at 19 miles per hour and…

A: The distance is changing at a rate of 29.499 miles per hour.

Q: Duterte and Bong Go on bikes are separated by 400 meters. Duterte starts riding north at a rate of 9…

A:

Q: Suppose that two boats leave a dock at different times. One heads due north, the other due east.…

A:

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.