The number of gallons of water, W, used when taking a shower varies directly as the time, t, in minutes, in the shower.A shower lasting 5minutes uses 30 gallons of water.How much water is used in a shower lasting 13 minutes?

Q: Lamont walks the 15 meters from the front door of his house to his car at a constant rate of speed.…

A:

Q: The number of gallons of water, W, used when taking a shower varies directly as the time, t, in…

A:

Q: In an electrical circuit, the current passing through a conductor varies inversely with the…

A:

Q: The volume, V, of a gas varies inversely as the pressure, P, on it. The volume is 2540 cm3  when the…

A:

Q: The time (T) it takes to plant rice in an acre varies inversely as the number of farm workers (W).…

A: The time (T) it takes to plant rice in an acre varies inversely as the number of farm workers (W).…

Q: A tank is filled with 400 gallons of brine with 25 % dissolved salt. 5 gallons of 20% salt solution…

A:

Q: A tank is filled with 400 gallons of brine with 15 % dissolved salt. 10 gallons of 20% salt solution…

A: Given datavolume of tank=400 gallonsAmount of salt=15% of 400=400*15100=60

Q: The current, I, in amperes, flowing in an electrical circuit varies inversely as the resistance, R,…

A: To Determine: The current, I, in amperes, flowing in an electrical circuit varies inversely as the…

Q: Stan and Hilda can mow the lawn in 40 min if they work together. If Hilda works twice as fast as…

A:

Q: Allen runs 8 miles in 3 hours at a steady pace. How long does it take him to run 3 miles?

A: speed is calculated by the formula,

Q: The square of x varies directly as the cube of y.  When x=2 and y=4, find y when x=8?

A: Given square of x varies directly as the cube of y, thus x2=ky3, where k is the constant of…

Q: The distance that Sarah travels varies directly to how long she drives. She travels 440 miles in 8…

A:

Q: A pot of boiling soup with an internal temperature of 100° Fahrenheit was taken off the stove to…

A:

Q: The number of kilograms of water in the human body varies directly with the mass of the human. A…

A:

Q: The length-weight relationship for the sei whale can be approximated by W = 0.0016L^2.43 , where W…

A:

Q: The volume of gas in a gas shock absorber varies inversely with the pressure and directly with the…

A:

Q: The amount of water required for a yard which has been landscaped for a desert environment is 17% of…

A: The value of x% of y is calculated using the formula below.

Q: The velocity, v, of a falling object varies directly to the time, t, the object is falling. After 3…

A: Follow the procedure given below.

Q: The volume,V cubic centimeters, of a melting snowball after t hours in the sun is given by the…

A:

Q: Devontre rode his bike uphill 5 miles and then back downhill. The rate at which Devontre traveled…

A: Let his uphill rate is = x mph So his downhill rate is = x+20  Distance= 5 miles in each case.

Q: The time required to do a job varies inversely as the number of peopelworking. It takes 5hr for 7…

A:

Q: Suppose the relationship between Y and X is given by: Y = 50 + 3X By how much does Y change if X…

A: Given,   The relationship between Y and X is given by,   Y = 50 + 3X   The objective is to find how…

Q: The distance s that an object falls varies directly with the square of the time, t, of the fall. If…

A: solve the following

Q: The number of kilograms of water in a human body varies directly as the mass of the body.  An 87​-kg…

A: to determine.

Q: Suppose the equation for the amount of water w (in gallons) in the pool after t hours is w=…

A: It is given that, if w is the amount of water (in gallons) in the pool after t hours, then w=…

Q: An object is thrown downward, with an initial speed of 16 ft/s, from the top of a building 192 ft…

A:

Q: The number of minutes needed to complete a job,m, varies inversely with the number of works, w. 8…

A: Form a equation and put the give values to find the constant and solve for unknown.

Q: The volume, V, of a gas varies directly as the temperature, t, and inversely as the pressure, P. At…

A:

Q: The velocity v of a falling object varies directly with the time t of the fall. If after 3 seconds,…

A:

Q: The number of gallons of water, W, used when taking a shower varies directly as the time, t, in…

A: Given:A Shower  lasting 5 minutes uses 5 gallons of water13 minutes=?

Q: The profit per acre from a grove of orange trees is given by x(270 – x) dollars, where x is the…

A: Given, The profit per acre from a grove of orange trees is given by x(270-x) dollars, x is the…

Q: The time, t, required to complete a job varies inversely with the number of people, P, working on…

A:

Q: The cost of a train ticket varies directly as the number of miles, M, of the trip. A 400-mile trip…

A: The cost of 400 mile trip is $180 We have to calculate the cost of 360 mile trip.

Q: Ella's motorboat can travel 35mi/h in still water. If the boat can travel 6 miles downstream in the…

A: Given:-Speed of motorboat in still water                = 35mi/h

Q: For a substance C, the time rate of conversion is proportional to the square of the amount of…

A: Given: For substance C, the time rate of conversion is proportional to the square of the amount of…

Q: Liana was 10 miles from home at 2 pm and 70 miles from home at 3:30 pm. What was her average rate of…

A:

Q: temperature of the object decreases from 100°C to 90°C in 10 minutes, how much longer will it take…

A: Given values Temperature of the surrounding, To= 25 degrees In the first case Initial temperature…

Q: The number of kilograms of water in a human body varies directly as themass of the body. A 96-kg…

A:

Q: It takes Manu twice as long to clean the pool as it takes Ander. If it takes Ander t hr to clean the…

A: Given:Manu takes twice as long as to clean the pool as it takes by Ander.Let Ander takes t hr to do…

Q: Jane has twice as much money invested at 5% annual intrest as she does at 4%. If her yearly income…

A:

Q: In an electrical circuit, the current passing through a conductor varies inversely with the…

A: I=current  R=resistance I∝1R to remove the proportionality sign we need to multiply constant k I=kR…

Q: Stan and Hilda can mow the lawn in 30 min if they work together. If Hilda works twice as fast as…

A: From given information ,

Q: How long will it take the snail to travel 11 meters will it be more or less the 40 minutes?

A:

Q: When building a house, the number of days required to build is inversely proportional to with the…

A: Number of days required to build is inversely proportional to with the number of workers. One house…

Q: The volume of water left in a reservoir as it empties is shown by the formula below, where V is the…

A:

Q: The number of kilograms of water in a human body varies directly as the mass of the body. A 90-kg…

A: Direct proportion is the relationship between two variables whose ratio is equal to a constant…

Q: Ben starts walking along a path at 4 mi/h. One and a half hours after Ben leaves, his sister Amanda…

A:

Q: A motorboat takes 3 hours to travel 108 miles going upstream. The return trip takes 2 hours going…

A: Let x be the speed of a motorboat in still water and y be the current rate.

Q: The value V of a Porsche 718 Cayman that is  t years old can be modeled by V(t) = 420,000(0.965)t…

A:

Q: The time, t, required to complete a job varies inversely with the number of people, p, working on…

A: Let J is the job T is the time taken P is the number of workers employed for the job. As per problem…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.