A man estimates that he can paint his house in x hours of his spare time if he buys equipment costing \frac {500 + 3000}{x^2} dollars, and that his spare time is worth $2 per hour. How many hours should he take (in order to minimize his total costs)? Hr
If you are paid a weekly base salary of $200 plus an hourly wage of $5.00, determine an equation for finding your weekly gross pay (P) for t hours. Specify a number of hours between 25 and 50 hours wo
The bill (parts and labor) for the repair of a car was $458. The cost of parts was $339. The cost of labor was $34 per hour. Write and solve an equation to find the number of hours of labor.
Two plumbers received a job. At first, one of the plumbers worked alone for 1 hour, and then they worked together for the next 4 hours. After this 40% of the job was finished. How long would it take e
An electrician charges a customer $260 for 4 hours. He charges one customer $150 for 2 hours. How much does he charge for his service fee, x, and his hourly charge, y, to his customers?
1. A man estimates that he can paint his house in x hours of his spare time if he buys equipment costing 100+\frac{5,000}{x^{2 dollars, and that his spare time is worth $2 per hour. How many hours
An engineer charges $60 per hour and his assistant receives $20 per hour. For a certain job, a client received a bill of $580. If the assistant worked for 5 fewer hours than the engineer, how much time did each one worked?
Julie needs to have a toilet repaired in her house. The cost of the new plumbing fixtures is $110 and labor is $70/hr. Write a model that represents the cost of the repair C (in $) in terms of the number of hours of labor x .
Oil leaks out of a tanker at a rate of r = f(t) gallons per minute, where t is in minutes. Write a definite integral expressing the total quantity of oil (in gallons) which leaks out of the tank
If you are paid an hourly wage of $9.00, determine an equation for finding your weekly gross pay (P) for t hours. Specify an amount between 25 and 40 hours worked for 1 week and determine your gross p
An auto repair shop charged a customer $390 to repair a car. The bill listed $75 for parts and the remainder for labour. If the cost of labour is $45 per hour, how many hours of labour did it take to repair the car? A. 6 hours B. 7 hours C. 8 hours D. 7.5
Company A charges $110 for the truck and $55 per hour for the movers. Company B charges $100 for the truck and $60 per hour for the movers. Create a cost equation for each company where y is the total
When three pipes fill a pool, they can finish in 12 hours. Two of the pipes can finish in 18 hours if they are working together. How long would it take a third pipe to fill the pool on its own?
You get paid a salary equal to $20/hour for a standard 40-hour work week and 1.5 times your hourly rate for each hour of overtime worked. \ a) Determine an equation for calculating your total pay in a week where overtime is worked. \ b) Solve the equ
The rate (in liters per minute) at which water drains from a tank is recorded at a half minute intervals. Use the average of the left and right endpoint approximations to estimate the total amount of water drained during the first 3 minutes. t \ (\tex
A water tank can be filled by an inlet pipe in 7 hours. It takes 2 times as long for the outlet pipe to empty the tank How long will it take to fill the tank if both pipes are open? Enter your answer as an integer or decimal number.
A roofing contractor purchases a shingle delivery truck with a shingle elevator for $42,000. The vehicle requires an average expenditure of $6.50 per hour for fuel and maintenance, and the operator is paid $11.50 per hour. (a) Write a linear equation givi
The Tomkins Company forecasts that total overhead for the current year will be $1,200,000 and that total machine hours will be 10,000 hours. Year to date, the actual overhead is $800,000 and the actual machine hours are 20,000 hours. If the Tomkins Compan
The rate (in liters per minute) at which water drains from a tank is recorded at half-minute intervals in the table below. Use the average of the left- and right-endpoint approximations to estimate the total amount of water drained during the first 3 minu
Villa Park PlumberAl's Rentals charges $25.00 per hour to rent a sailboard and a wet suit. Wendy's Rentals charges $20.00 per hour plus $15.00 extra for a wet suit. Find the number of hours for which the total charges
The exterior of a house needs to be painted. Bill's crew can paint the house in 12 hours, while it would take Ted's crew 14 hours to paint the house. Bill's crew starts the job for 3 hours before being joined by Ted's crew. What is the total amount of tim
Oil leaks out of a tanker at a rate of r = f(t) gallons per minute, where t is in minutes. Write a definite integral expressing the total quantity of oil which leaks out of the tanker in the first hou
(a) Suppose you have a job that pays $10 per hour. Write a function, g than can be used to determine your gross pay (your pay before taxes are taken out) per hour, h, that you worked. (b) Now let's write a formula for how much money you'll actually take h
The table of values below shows the rate of water consumption in gallons per hour at selected time intervals from t = 0 to t = 12. Using a Trapezoidal sum with 5 subintervals, estimate the total amoun
I hired a carpenter and an apprentice to do some work at my business. They worked two days. On the first day I was billed $210 for 11 hours of work by the main carpenter and for 7 hours of work by the apprentice. On the second day I was billed $114 for 3
The rate (in liters per minute) at which water drains from a tank is recorded at half-minute intervals. Use the average of the left- and right-endpoint approximations to estimate the total amount of water drained during the first 3 min.
Mickey charges $15, $30, $45, and $60 for babysitting 1, 2, 3, and 4 hours, respectively. Is the relationship between the number of hours and the amount charged proportional? If so, find the unit rate. If not, explain.
The cost (in dollars) of repainting a car is given by C(x, y) = 4 x^2 + 5 y^2 - 4 x y^2 + 50 where x is the number of hours of labor and y is the number of gallons of paint used. Find the cost of 10 hours of labor and 8 gallons of paint.
When Raw Materials, Work in Process, and Finished Goods are recorded and carried at their standard cost, the fixed overhead applied to work in process is calculated by multiplying the predetermined overhead rate by the actual direct labor-hours worked. Tr
Thomas is having a deck built on the back of his house. A local building supply store has quoted him $1000 for materials plus a carpenter's wage of $30/hour. a) Write a word equation that describes the relationship between the cost of the job and the num
A water tank can be filled by an inlet pipe in 10 hours. It takes 3 times as long for the outlet pipe to empty the tank. How long will it take to fill the tank if both pipes are open?
A water tank can be filled by an inlet pipe in 8 hours. it takes 3 times as long for the outlet pipe to empty the tank. How long will it take to fill the tank if both pipes are open?
A water tank can be filled by an inlet pipe in 7 hours. It takes 2 times as long for the outlet pipe to empty the tank. How long will it take to fill the tank if both pipes are open?
A water tank can be filled by an inlet pipe in 6 hours. It takes 3 times as long for the outlet pipe to empty the tank. How long will it take to fill the tank if both pipes are open?
A full tank initially (at t = 0) contains 16 gallons. Then, water is removed at a rate of (1 + t) gallons per minute, where t is the time in minutes. Find the time, t, where the tank is half empty.