A passenger train leaves a train depot two hours after a freight train leaves the same depot. The freight train is traveling 20 mph slower than the passenger train.  Find the rate of the passenger train if the passenger train overtakes the freight train after 3.2 h

Q: A cruise ship can sail 26 mph in calm water. Sailing with the Gulf Stream, the ship can sail 160 mi…

A: Given,          A cruise ship can sail 26 mph in calm water. Sailing with the Gulf Stream, the ship…

Q: A small radio transmitter broadcasts in a 55 mile radius. If you drive along a straight line from a…

A:

Q: A passenger train leaves a train depot 2 h after a freight train leaves the same depot. The freight…

A:

Q: A plane flying with the jet stream flew from Los Angeles to Chicago, a distance of 2572 mi, in 4 h.…

A:

Q: The speed of a boat in still water is 25 mph.  The jacksons traveled 70 mi down the woodser River in…

A: Given that,  The speed of a boat in still water is 25 mph The distance traveled by Jacksons to…

Q: The table gives the outside temperature in degrees Fahrenheit on a winter day in Death Valley,…

A: In this case , Average rate of change is ratio of difference in temperature to difference in time

Q: A passenger train traveled 120 miles in the same amount of time it took a freight train to travel 70…

A: Use the relationship among time, distance and speed and solve the question.

Q: A turboprop plane flying with the wind flew 700 mi in 5 h. Flying against the wind, the plane…

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Q: A small radio transmitter broadcasts in a 54 mile radius. If you drive along a straight line from a…

A: The radio transmitter broadcasts in a radius of 54 miles. One city is 65 miles north to the…

Q: A car traveled 50 miles in 40 minutes. Assume that the car will continue at this constant rate of…

A: We calculate distance travel in one hour.Then find the equation.

Q: A cruise ship made a trip of 385 mi in 15 h. The ship traveled the first 105 mi at a constant rate…

A: Speed= distance/time

Q: Which situation 100 miles in 3 hours represents a constant rate of change of 50 miles per hour? 180…

A: which situation represent constant rate of change of 50 miles per hour

Q: In still water, your small boat average is 8 miles per hour. It takes you the same amount of time to…

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Q: The speed of a boat in still water is 15 mph. The jacksons traveled 60 mi down in the woodset River…

A:

Q: A passenger train leaves a train depot 1 h after a freight train leaves the same depot. The freight…

A: Solution : Let , the speed of the passenger train be xmphsince , the freight train is travelling 12…

Q: Lucy plants 29 flowers in 2 hours how do you find the constant rate

A: Total flowers planted in 2 hours = 29

Q: A cyclist and a jogger start from a town at the same time and head for a destination 6 mi away. The…

A: framing equation in one variable and solve

Q: A passenger train leaves a train depot two hours after a freight train leaves the same depot. The…

A: Let the rate of the passenger train is x mph, then the rate of a freight train is (x-20)mph. And…

Q: The distance that an object falls when it is dropped is directly proportional to the square of the…

A: Let, d is the distance and t is the timethe object has been falling    Since, the distance that is…

Q: a snow plow has a maximum speed of 60pmhon a dry highway. its maximum speed decreases by 1.3mph for…

A: Let x inches will stop the snowplow. 1 inch decreases 1.3 mph. x inch decreases 1.3x mph. The…

Q: A small radio transmitter broadcasts in a 47 mile radius. If you drive along a straight line from a…

A: Given: A small radio transmitter broadcasts in a 47 miles radius and driving along a straight line…

Q: A missile flies 40 miles in 20 minutes. Calculate the missile’s rate of change

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Q: Mulder and scully are driving to the same town. Mulder leaves the office at 9:30 AM. Averaging 55…

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Q: the area of a square is increasing at a rate of 42 centimeters squared per second. find the rate of…

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Q: A cruise boat travels 12 miles downstream in 2 hours and returns to its starting point upstream in 6…

A: closest option to the answer is C

Q: car starts from a point at 2:00 p.m. and travels north at 40 mph. Another car starts from the same…

A: Given query is to find the rate of change of distance between the cars.

Q: (a) Find the rate of change of the volume when r = 12 inches. in.3/min (b) Find the rate of change…

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Q: A company's revenue from selling å units of an item is given as R. = 1500x – x². If sales are…

A:

Q: The way Professor Waner drives, he burns gas at the rate of 1 −e-t gallons each hour, t hours after…

A: Given that the gas burnt at the rate of, R't=1-e-t

Q: Investment The simple interest earned in 9 yearsis directly proportional to the interest rate r. If…

A:

Q: Wind resistance is jointly proportional to velocity and surface area of the object. If an object is…

A: Given,Wind resistance is jointly proportional to velocity and surface area of the objectLet w, v,…

Q: The volume of a sphere is decreasing at a constant rate of 4011 cubic inches per second. At the…

A:

Q: A small radio transmitter broadcasts in a 53 mile radius. If you drive along a straight line from a…

A:

Q: A scuba diver dove from the surface of the ocean to an elevation of -49. feet at a rate of -14.3…

A:

Q: Flying against the wind, an airplane travels  3400  kilometers in  5  hours. Flying with the…

A:

Q: The volume of a cube decreases at a rate of 0.3 ft/min. What is the rate of change of the side…

A: Given: Volume of cube decreases at a 0.3ft3/min that is dVdt=0.3ft3/min side length is 7ft that is…

Q: andre ran 2 kilometers in 15 minutes and jada ran 3 kilometers in 20 minutes both ran at a constant…

A: Given that  andre ran 2 kilometers in 15 minutes and jada ran 3 kilometers in 20 minutes both ran at…

Q: The volume of a cube decreases at a rate of 0.3 ft° / min. What is the rate of change of the side…

A: We can solve the given problem by using the concept given  below. If f(x) is the given function…

Q: The profit (P) realized by a company varies directly as the number of products it sells (s). If a…

A:

Q: The altitude of a triangle is increasing at a rate of 2 centimeters/minute while the area of the…

A:

Q: A motorboat traveling with the current went 36 mi in 2 h. traveling against the curretn it took 3 h…

A:

Q: Give an example of a increased rate and a decreased rate

A: Increased and decreased rate with proper example are as follows.

Q: The amount of time it takes a swimmer to swim a race is inversely proportional to the average speed…

A: It is given that time∝1speed Let t = time s=speed t∝1st=ks

Q: A person x inches tall has a pulse rate of y beats per minute, as given approximately by -1/2 y=598x…

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Q: A boater travels 45 miles per hour on the water on a still day. During one particularly windy​ day,…

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Q: The rate of the jet streams is 100 miles ph. Travelling  with a jet stream,an airplane can  fly 1200…

A: To find the average rate of airplane in calm air  Given : The rate of the jet streams is 100 miles…

Q: A 3.5 cu. inch car air freshener is losing volume at a rate of 1%/day. Find the volume after 30…

A: To find the volume after 30 days.

Q: A stone is thrown vertically upward with a velocity of 40 feet per second from the top of a tower…

A: Solution ) u = 40ft/ sec , s = 200ft We know from newton law  v = u + gt  When we throw and stone…

Q: With the current, a boat can travel 84miles in 2hiurs. Against the current the same trip takes 3…

A: To form equations for the required speeds and solve for them

Q: A motorboat can maintain a constant speed of 46 miles per hour relative to the water. The boat makes…

A: Let x =speed of the current (46-x)=speed upstream (46+x)=speed downstream

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.