Questions on Word Problems: Rate of work, PAINTING, Pool Filling answered by real tutors!

Tutors Answer Your Questions about Rate-of-work-word-problems (FREE)

Question 363280: i paint a house in 4 hours and my wife paints the same house in 6 hours how long does it take for us to paint the house together?
i have not been in scholl for over 20 yrs and need a reminder of the equations
Click here to see answer by jim_thompson5910(35256)

Question 363386: Write an equation of the line passing through (-3,13),(8,9), and (-8,23).
I wasn't sure how to do this because they have different slopes.
The slope of (-3,13) and (8,9) is 4/-11
The slope of (8,9) and (-8,23) is 7/-8
How would I write an equation for that?
Click here to see answer by jim_thompson5910(35256)

Question 363384: A real estate sales agent recieves a salary of $275 per week plus a commission of 1.5% of sales. Write an equation that gives the weekly income of y in terms of sales x.

Click here to see answer by rfer(16322)

Question 363408: The space of polynomials in one variable, x, of degree at most 4, is mapped into itself by the linear map, L, that takes a typical polynomial P to the polynomial x(dP/dx)-4P, where dP/dx denotes the standard derivative of P.
Thus: L(P)= x(dP/dx) - 4P
1. Prove (show) that L is a linear map.
2. Wat is the kernal of this map? (i.e. describe the polynomials that it contains)
3. What is the dimension of the kernal?
4. What is the dimension of the range of this map?
5. Is there a polynomial of degree 2 that is not in the range of the map? give reasons for your answers to questions 2-5
Click here to see answer by robertb(5830)

Question 363816: I'd like someone to show me how to you work out this problem I know the answer I'm just not sure how I got it and I'm trying to help my niece learn it so I'd like to show her how to work it out. The problem is below
Working together, Paul and Daniel can pick forty bushels of apples in 4.95 hours. Had he done it alone it would have taken Daniel 9 hours. Find out how long it would take Paul to do it alone.
I'll wait to hear from someone,
Thanks
Click here to see answer by Alan3354(69443)

Question 364018: Solve the following problem algebraically. That is, set up an equation and solve it. Be sure to label clearly what the variable represents.
A bricklayer can complete a wall in 7 days, whereas his assistant can do the same size wall in 3 days. Working together, how long will it take for them to complete the wall?
Click here to see answer by robertb(5830)

Question 364029: A pool can be filled by a pipe in 3 hours. It takes 3 times as long for another pipe to empty the pool. How long will it take to fill the pool if both popes are open?
How do you figure out this problem... I eventually found the answer but need to learn how to do it the right way.
Click here to see answer by Fombitz(32388)

Question 364294: one speed skater starts across a frozen lake at 8 meters per sec. 10 sec later a second skater starts from the same point in the same direction at 10 meter per sec. how many sec after the second skater starts will she catch the first skater.
i know the answer to the problem. it is 40 sec. i just don't know how to get it
Click here to see answer by Alan3354(69443)

Question 364522: Two pipes are pumping water into a 1200 gallon well. If the first pipe can pump water at the rate of 48 gallons per hour and the second pipe can pump water at the rate of 192 gallons per hour, in how many hours will the well be filled?
Click here to see answer by nerdybill(7384)

Question 365062: karla, pam, and sandy working together can do a job in two hours. karla and pam working together can do a job in four hours. pam and sandy can do a job in three hours. how long does it take for each person to do the job working alone? how long does it take karla and sandy working together to do the job?
Click here to see answer by ankor@dixie-net.com(22740)

Question 365335: After Hurricane Bob, the Duvals needed to remove water from thier flooded basement. They had a sump pump and borrowed a second from a local fire department. The chief explained that he expects both pumps working together will empty the basement in 6 hours. The fire dept. sump pump has a higher horsepower and would empty the basement itself in 2 hours less time than the Duval's pump alone. how long would it take each pump to empty the cellar if each were working alone?
Click here to see answer by stanbon(75887)

Question 365382: It takes 3 gallons of paint to cover 4 rooms, how many gallons will it take to paint 50 rooms?

Click here to see answer by Alan3354(69443)

Question 365362: A Master contractor and his apprentice could spackle the interior walls of a new home in 18 hours. The master contractor figures he would have finished the job himself about 5 hours faster than his apprentice. How long would it take each of them to complete the job solo?
If the master contractor earns $45 per hour and the apprentice earns $28.50 per hour and time is not an issue explain one way the construction company could save? Show work.
Click here to see answer by ankor@dixie-net.com(22740)

Question 365542: how many gallons of water would it take to fill a ditch that is 15' wide, 5' deep, and 30' long?
Click here to see answer by Alan3354(69443)

Question 365271: A town's old street sweeper can clean the streets in 60 hours. The old sweeper together with a new sweeper can clean the streets in 15 hours. How long would ti take the new sweeper to do the job alone?
Click here to see answer by scott8148(6628)

Question 366146: Maria Vazquez and La Toya Johnson Plant petunias in a botanical garden. It takes Maria twice as long as Latoya to plant the flowers. Working together, they can plant the flowers in ten hours. How long does it take Latoya to plant the flowers by herself?
Click here to see answer by ewatrrr(24785)

Question 366587: There are 630 dishes that need to be rinsed. John can rinse them in 70 minutes by himself. It will take his friend Bob 105 minutes to rinse these dishes. How long will it take them if they rinse these 630 dishes together?
Click here to see answer by nyc_function(2741)

Question 366781: If it takes 4 workers 6 hours each to pave a road, how many hours will it take 12
workers to complete the same job?
(A) 2 (B) 3 (C) 6 (D) 8 (E) 18
Click here to see answer by amoresroy(361)

Question 366898: John can complete the job in 6 hours, and Sue can complete the job in 4 hours. How long does it take them to complete the job when they work together?

Click here to see answer by ewatrrr(24785)

Question 366864: Dal and Kim can assemble a swing set in 1 and 1/2 hours. Working alone it takes Kim 4 hours longer than Dal to assemble the swing set. How long would it take Dal, working alone, to assemble the swing set? I have tried everything I could to solve this one and haven't had any luck. I would appreciate anyone's help! Thank you for your time!
Click here to see answer by ptaylor(2198)

Question 366852: One hose fills a tank in T hours. Another hose fills the same tank in T/2 hours. If both hoses work at the same time, the tank is filled in 12 hours. What is T?
Click here to see answer by ptaylor(2198)

Question 367053: a can finish a job in 3 hour and b can finish the same ob in 6 hours. how long will it take both of them working together to finish the job?
Click here to see answer by mananth(16946)

Question 367472: Using one drain a swimming pool can be emptied in 45 minutes. Using a different drain the job requires one hour and fifteen minutes how long would it take if both drains were open
Click here to see answer by Fombitz(32388)

Question 367854: Timothy can mow his lawn in 40 minutes, but his brother Shamus needs only 30 minutes to mow the same lawn. If they work together on the lawn, how long will it take them to finish mowing?
Click here to see answer by nerdybill(7384)

Question 368342: Working alone, Ryan can dig a 10 ft by 10 ft
hole in five hours. Castel can dig the same
hole in six hours. How long would it take
them if they worked together?
Click here to see answer by nerdybill(7384)

Question 368805: I need help solving this problem.
There is a table given that says weight in pounds, x: 5,10,15
then cost to mail, y: $7, $11, $15
then it asks..
How much does it cost per pound to mail a package?
Then.. What would a 16 pound package cost to mail?
Thanks for the help!
Click here to see answer by stanbon(75887)

Question 368906: Need help with this problem
A long distance telephone company offered a flat rate of 9 cents per minute, with a 50 cent minimum charge per completed call. Find the cost in cents per minute for a 22 minute call?
I got .44 is that correct?
Click here to see answer by mananth(16946)

Question 368952: He spends 18 hours to finish 40% of a job, how lond will it take to finish the whole job?
Click here to see answer by mananth(16946)

Question 370282: an experienced painter can paint a picket fence in 20 hours. An apprentice painter can do the same job in 45 hours. How long would it take to paint the fence of both painters worked together?
Click here to see answer by mananth(16946)

Question 370254: Caleb is having a very hard time coming up with ideas for math problems. He normally comes up with them at a rate of three per hour, but when he starts listening to music he slows down to a rate he cannot determine.
today he has to make up twelve problems. He alterates between one hour with the music and one hour without, starting with it on. If it takes him 5 hours to complete the problems, how many problems can he make up in an hour while listening to music?
Click here to see answer by mananth(16946)

Question 370333: An express train travels 520 miles in the SAME AMOUNT OF TIME in which a freight train travels 320 miles. The rate of the express train is 25mph faster than the rate of the freight train. Find the rate of the express train and the rate of the freight train?
Click here to see answer by amoresroy(361)

Question 370264: Aimee mows lawns at a rate of 30 square feet per minute, Judy mows at 40 square feet per minute, and sue mows 60 square feet per minute. They accept a job that requires they mow 22,400 square feet of lawn. Aimee begins mowing at 7 am but Judy does not begin for another 15 minutes. Sue begins mowing at 8:45am and they finish together. To the nearest minute, how long did Judy work?
Click here to see answer by edjones(8007)

Question 370440: Two pipes can fill a tank in two hours it the first tank three hours longer than the second tank. How long would it take each pipe alone?
thank you
Click here to see answer by ewatrrr(24785)

Question 370549: The sum of two numbers is 52, and their difference is two less than the smaller number. What are the two numbers?
Click here to see answer by ankor@dixie-net.com(22740)

Question 370611: A heating system can increase the temperature of a classroom by 3 degrees Celsius per hour. If the class room temperature is 15 degrees Celsius when the timer starts the heating system during the night, which of the following equations provides a mathematical model for the temperature after t hours.
A.Temperature= 3t-15
B. Temperature= 3t+15
C. 3t/15
D. 3t times 15

/= fraction
Click here to see answer by mananth(16946)

Question 371009: Aubrey uses a slingshot to shoot a marble from a window. The height of the marble h(t) in feet at time t seconds is given by the function h(t)=-16t square -50t+164. How many seconds elapse before the marble hits the ground?
Click here to see answer by nerdybill(7384)

Question 371318: A panda can eat the leaves from a certain bamboo stem in 14 minutes. Together, two pandas could eat the leaves from that same stem in 9 minutes. how long would it take the second panda to eat the leaves from the stem by itself?
Click here to see answer by amoresroy(361)

Question 371768: Thank you very much to anyone who solves this problem. The pool can be filled in 8 hours and 30 minutes with a red hose. If I run a red and a green hose together, the pool can be filled in 5 hours and 15 minutes. How long would it take to fill up the pool with the green hose only?
Click here to see answer by ankor@dixie-net.com(22740)

Question 372353: I don't know how to set up the equation for this word problem...
My cat Archimedes can rid my garage of mice twice as fast as my neighbor's cat, Pythagoras. If they joined forces, they can clear a garage in a mere two hours. In how many hours does it take for each of these felines to clear a garage of mice working alone?
I think the known values are:
Pythagoras's rate = x
Archimedes' rate = 2x
Total time working together = 2 hours
Thank you!

Click here to see answer by stanbon(75887)

Question 372422: One hose can fill a goldfish pond in 45 minutes, and two hoses can fill the same pond in 20 minutes. How long does it take the second hose alone to fill the pond?
Click here to see answer by nyc_function(2741)

Question 372470: A bathtub can be filled by cold water faucet in 7 minutes and by the hot water faucet in 10 minutes. How long does it take to fill the tub if both faucets are open?

Click here to see answer by user_dude2008(1862)

Question 372466: Two pipes are used to fill an oil tanker. When the larger pipe is used alone, it takes 60 hours to fill the tanker. When the smaller pipe is used alone, it takes 80 hours to fill the tanker. The large pipe begins filling the tanker. After 20 hours, the large pipe is closed and the smaller pipe is opened. How much longer will it take to finish filling the tanker using only the smaller pipe?
Click here to see answer by mananth(16946)

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