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 140306: If a Home Depot worker can paint a house in 4 hours, and a Lowes worker can paint the same house in 6 hour, how long will it take for both of them to paint the house together?
Click here to see answer by stanbon(57307)

Question 141301: Bob and Tom are mowing a yard which is 80' X 40'. They will each mow 1/2 of the yeard. They must mow the yeard in a spiral. How far in does Bob mow before turning it over to Tom? What equation is used to solve this?
Click here to see answer by checkley77(12569)

Question 141335: The intake pipe can fill a tank in 4 hours when the outlet pipe is closed, but with the outlet pipe open it takes 6 hours. How long would it take the outlet pipe to empty a full tank?
Click here to see answer by scott8148(6628)

Question 141507: This question was on testprepreview.com which I was using to practice for the COMPASS test. My answer is different from what they say the correct answer is. Could you please show me the step by step solution?
"If Sally can paint a house in 4 hours, and John can paint the same house in 6 hours, how long will it take both of them to paint the house together?" I figured Sally could paint 1/4 of the house in 1 hour and John could paint 1/6 of the house in 1 hour. So I added them together to get they could paint 5/12 of the house in 1 hour. I figured if they could paint 5/12 of the house in 1 hour then to paint 12/12 of the house, the whole thing would take 2 1/6 hours, which is 2 hours and 10 minutes. They gave the correct answer as 2 hours and 24 minutes. I need to understand how they worked this. Thank you.
Joyce M. Smith
( a new college student at age 62)
Click here to see answer by checkley77(12569)

Question 142184: Bob can fill the pool in 15 minutes. Fred can fill the pool in 10 minutes. How long will it take Bob and Fred to fill the pool together?
Click here to see answer by scott8148(6628)

Question 142743: An electrician and his apprentice working together, complete the wiring of a building in 20 days. If the apprentice were to do the work on his own he would take 9 days longer than the electrician. How long would it take each of them if they did the work on their own.
Click here to see answer by ptaylor(2048)

Question 112922: Ricky can install a basic security system in 4 hours. If it takes Ricky and Mark 2 hours working together to install this system, how long does it take Mark working alone?
Click here to see answer by awang1996(50)

Question 143225: If you can type 1 page in 3 minutes how many pages can you type in 5 minutes?
Click here to see answer by solver91311(16877)

Question 143224: If it takes sally 4 hours to paint house and Jim 6 hours to paint house. how long will it take to paint house together?
Click here to see answer by solver91311(16877)

Question 143248: Together Mary and Sara can mow a golf course in 15 hours. Alone it takes Mary 2 hours less than Sara. Find the time it takes each of them to mow the course alone. PLEASE HELP!!!! the answer is m=29 and s=31, but I don't know how to get there. HELP APPRECIATED!!!!
Click here to see answer by scott8148(6628)

Question 143303: One drain can empty a storage tank in 8.5 hours. When this drain is used along with a second drain, the tank can be emptied in 5 hours. How long(to the nearest 0.1 hour) would it take the second drain, working alone, to empty the tank?
Click here to see answer by stanbon(57307)

Question 143343: 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 how long it would take Paul to do it alone?
Click here to see answer by ptaylor(2048)

Question 143381: Pipe A can fill a tank in 2 hours and Pipe B can fill ii in half the it takes Pipe C to empty it. When all 3 are opened, it takes 1.5 hours to fill the pool. How much time is required for Pipe C to empty the tank? PLEASE HELP! The answer is 6 hours, but I don't know how to get there. HELP MUCH APPRECIATED!!
Click here to see answer by ankor@dixie-net.com(15649)

Question 143414: Pipe A can fill a tank in 2 hours and Pipe B can fill ii in half the it takes Pipe C to empty it. When all 3 are opened, it takes 1.5 hours to fill the pool. How much time is required for Pipe C to empty the tank? PLEASE HELP! The answer is 6 hours, but I don't know how to get there. HELP MUCH APPRECIATED!!
Click here to see answer by ptaylor(2048)

Question 143464: Can you help me with this problem. Five painters can paint 5 houses in 5 days. At that rate, how many days will it take 2 painters to paint 1 house?
Click here to see answer by stanbon(57307)

Question 144970: If tbone can paint a car in 4 hours and walker texas ranger can paint the same car in 6 hours, how long will it take them to paint the car together?
Click here to see answer by jephkapi(1)

Question 145100: It takes Brandon 3 hours to paint a house. It takes Hasan 5 hours to paint the same house. How long will it take Brandon and Hasan to paint that same house together?
Click here to see answer by vleith(2825)

Question 145847: Hi, I am having difficulty putting this problem into an equation even though I know the answer.
Workman A and B complete a certain job if they work together for 6 days or if A alone works for 3 days and B alone works for 10 days. How long does it take each man to complete the job alone?
The answer is A - 10 1/2 days and B - 14 days
Thank you for your help.
Click here to see answer by ankor@dixie-net.com(15649)

Question 146208: alright and the last one for tonight !
Jim can fill a pool carrying buckets of water in 30mins. Sue can do the same job in 45mins. Tony can do the same job in 1 1/2 hours. How quickly can all three fill the pool together?
a.12 minutes
b.15 minutes
c.23minutes
d.28 minutes
e.21 minutes
thank you and good night!
Click here to see answer by ptaylor(2048)

Question 146242: If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks?
A. 2 minutes and 44 seconds
B. 2 minutes and 58 seconds
C. 3 minutes and 10 seconds
D. 3 minutes and 26 seconds
E. 4 minutes and 15 seconds

Click here to see answer by Earlsdon(6287)

Question 147599: This word problem needs to be solved using a rational expression, thank in advance for the help. The current of a river is 2 miles per hour. A boat travels to a point 8 mile upstream and back again in 3 hours. What is the speed of the boat in still water?
Click here to see answer by scott8148(6628)

Question 147660: first let me thank you all for your help. my problem is A,B and C can finish a job in 6 days if B and C work together the job will take 9 days if A and C work together the job will take 8 days in how many days can each man working alone do the job? again thank very much for your help
Click here to see answer by stanbon(57307)

Question 147917: Sally paints a house in 4 hours, jill paints the same house in 6 hours, how long does it take them to paint the house together?
Click here to see answer by ptaylor(2048)

Question 148363: An experienced carpenter can panel a room 3 times faster than an apprentice can. Working together, they can panel the room in 6 hours. How long would it take each person working alone to do the job?
Click here to see answer by ptaylor(2048)

Question 148508: Suppose it takes Tom and Dick 2 hours to do a certain job, it takes Tom and Harry 3 hours to do the same job. It takes Dick and Harry 4 hours to do this same job.
How long will it take Tom, Dick, and Harry to do the same job together?
So, just for organizing:
T + D = 2hrs
T + H = 3hrs
D + H = 4hrs
T+D+H = ? hrs
Therefore: (I think, but I'm sure it's most probably right)
1/T + 1/D =1/2
1/T + 1/H =1/3
1/D + 1/H =1/4
1/T + 1/D + 1/H =1/x
So far, I got to T=12/5 and D=12
using reciprocals and the first equation, the sum is 6/12 or 1/2; so far so good.
But I've tried using it to solve for the H one.. and it doesn't quite work.. so when I get to the last equation I still have two variables, H and X.

Click here to see answer by ptaylor(2048)

Question 148509: Suppose it takes Tom and Dick 2 hours to do a certain job, it takes Tom and Harry 3 hours to do the same job. It takes Dick and Harry 4 hours to do this same job.
How long will it take Tom, Dick, and Harry to do the same job together?
So, just for organizing:
T + D = 2hrs
T + H = 3hrs
D + H = 4hrs
T+D+H = ? hrs
Therefore: (I think, but I'm sure it's most probably right)
1/T + 1/D =1/2
1/T + 1/H =1/3
1/D + 1/H =1/4
1/T + 1/D + 1/H =1/x
So far, I got to T=12/5 and D=12
using reciprocals and the first equation, the sum is 6/12 or 1/2; so far so good.
But I've tried using it to solve for the H one.. and it doesn't quite work.. so when I get to the last equation I still have two variables, H and X.

Click here to see answer by stanbon(57307)

Question 148609: Suppose it takes Tom and Dick 2 hours to do a certain job, it takes Tom and Harry 3 hours to do the same job. It takes Dick and Harry 4 hours to do this same job.
How long will it take Tom, Dick, and Harry to do the same job together?
So, just for organizing:
T + D = 2hrs
T + H = 3hrs
D + H = 4hrs
T+D+H = ? hrs
Therefore: (I think, but I'm sure it's most probably right)
1/T + 1/D =1/2
1/T + 1/H =1/3
1/D + 1/H =1/4
1/T + 1/D + 1/H =1/x
So far, I got to T=12/5 and D=12
using reciprocals and the first equation, the sum is 6/12 or 1/2; so far so good.
But I've tried using it to solve for the H one.. and it doesn't quite work.. so when I get to the last equation I still have two variables, H and X.

^
I posted this before, and my teacher said the answer was wrong. I used ptaylor's solution and method rather than Stan H's solution. seeing as we're looking for hours. anyway, I inverted 24/13 to 13/24 which is approx half an hour vs almost two hours. I'm sure that's the right solution since my teacher said 1 hr and 51 mins is too long.

Any comments?
Click here to see answer by scott8148(6628)

Question 149525: Gian and Arwin can finish a project in 4 2/3 hours. Gian can do it alone in half as much as time arvin can do the job. how long will it take arwin to do the job alone.
Click here to see answer by ptaylor(2048)

Question 149524: urgent..
working together, alice and betty can do a certain job in 4 1/3 days. but alice felt ill after 2 days of working and betty finished the job continuing to work alone in 6 3/4 more days. how long would it take each to do the job if each of them worked alone?
thnx for the help
Click here to see answer by ptaylor(2048)

Question 149620: It takes 4 minutes for the faucet to fill a sink. It takes 3 minutes for the drain to empty the sink. The sink is full, if the drain is open and the faucet turned on at the same time, how long does it take to empty the sink?
Click here to see answer by ptaylor(2048)

Question 149944: Working together, a painter and the painter's apprentice can paint a room in 4h. Working alone, the apprentice requires 7 more hours to paint the room that the painter requires working alone. How long does it take the painter, working alone, to paint the room? Please round your answer to one decimal place.

4/T + 4/T+7 = 1
T(T+7)(4/T + 4/T+7) = T(T+7)1
(T+7)4+4T = T(T+7)
4T +28 +4T = T^2 +T7
8T+28=T^2+T7

Am I doing this right? I keep coming up with the wrong answer, I think.
Click here to see answer by scott8148(6628)

Question 150111: Gail can type a chapter book in 4 hours jack can type a chapter book in 10 hours. How long would it take them to type a chapter book together?
Click here to see answer by stanbon(57307)

Question 150241: Pipe A fills a 50-liter tank at a rate of 15 liters per hour. Pipe B fills the same tank at a rate of 10 liters per hour. Pipe A runs alone for 100 minutes then the two of them together finish filling up the tank. How long does the whole operation take?
The answer is 160 minutes, but I have no idea how to arrive at this answer. Thank you!
Click here to see answer by jojo14344(1512)

Question 150250: If Sally can paint a house in 4 hours, and John can paint the same house in 6 hours, how long will it take for both of them to paint the house together?
Click here to see answer by checkley77(12569)

Question 150510: gian and arwin can finish a project in 4 2/3 hours. gian can do it alone in half as much time as arwin can do the job. How long will it take Arwin to do the job alone.
Click here to see answer by christopherbenner(2)

Question 150509: working together, alice and betty can do a certain job in 4 1/3 days. but alice fell ill after 2 days of working and betty finished the job continuing to work alone in 6 3/4 more days. how long would it take each to do the job if each of them worked alone?
Click here to see answer by ankor@dixie-net.com(15649)

Question 150560: Janet and Carl decorate cakes in a bakery. Janet can decorate a cake every 0.24 hour and Carl can decorate a cake every 0.33 hour. If they work together, at what rate are they decorating cakes? Round to the nearest tenth of a cake per hour.

Click here to see answer by ankor@dixie-net.com(15649)

Question 150565: roma can finish weeding a flower garden in 4 1/2 hours. roma has worked for 2 hours before amor joined her and they finished the job in 2 hours. how long would it take both of them to finish the job working together? how long would it take amor to do the job alone?
Click here to see answer by josmiceli(9671)

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