S paints house in 4 hrs, T in 6 hrs; find time if they work

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lynnettemorales

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I am trying to figure out how to solve this type of problem. I f anyone can offer me any help I would appreciate it.

If Sue can paint a house in 4hrs and Tom can paint the same house in 6hrs how many hrs will it take them to paint the house together?
 
Re: word problem ??

Figure out how much of the house Sue can paint in 1 unit of time. In one hour Sue can paint 1/4 of the house. (Must be a doll house, or even a dog house.) Figure out how much of the house Tom can pain in one hour. Using that info, since they are working together, you can say that in one hour so much (a certain fraction of the house) of the house is painted. With that information you can determine how long it will take to paint the whole house.
Example: if Joe, Tom and Bill can weed 1/4 of the garden in one hour, then they can weed the whole garden in 4 hours.
If they can dig 3/8 of a certain size trench in 1 hour, then they can dig the whole trench in 1/(3/8) or 8/3 hours.
 
Re: word problem ??

So I get that together they can paint 5/12 of the house in 1 hour and 10/12 of the house in 2 hours leaving 2/12 right?? But the how do you change the 2/12 into minutes. I can only guess it to be 1/6 by going from 2/12=10/60 or 1/10 but I know the answer is 2 hrs and 24 minutes.
 
2 2/12 hours is not correct.

Algebraically...
Decide what x represents. Name things.
Let x represent time it takes to paint the house when they are working together.
Then 1/x represents how much of the house is painted in 1 hour.
Now, 1/4 is amount of house that Sue paints in one hour.
1/6 is amount of house that Tom paints in one hour.
Build your equation on idea that in one hour amount painted by Sue plus amount painted by Tom equals the amount painted together.
Solve for x.
 
Re: word problem ??

lynnettemorales said:
So I get that together they can paint 5/12 of the house in 1 hour and 10/12 of the house in 2 hours leaving 2/12 right?? But the how do you change the 2/12 into minutes. I can only guess it to be 1/6 by going from 2/12=10/60 or 1/10 but I know the answer is 2 hrs and 24 minutes.
Click to expand...
Yes, 2/12 left; but that's 2/12 of job;
You know that 5/12 of job takes 1 hour, or 60 minutes:
so simply calculate what 2/12 is; ok?
 
I am trying to figure out how to solve this type of problem. I f anyone can offer me any help I would appreciate it.

If Sue can paint a house in 4hrs and Tom can paint the same house in 6hrs how many hrs will it take them to paint the house together?

Just another thought:

If it takes one person 5 hours to paint a room and another person 3 hours, how long will it take to paint the room working together?

Method 1:

1--A can paint a room in 5 hours.
2--B can paint a room in 3 hours.
3--A's rate of painting is 1 room per A hours (5 hours) or 1/A (1/5) room/hour.
4--B's rate of painting is 1 room per B hours (3 hours) or 1/B (1/3) room/hour.
5--Their combined rate of painting is therefore 1/A + 1/B = (A+B)/AB = (1/5 + 1/3) = (8/15) rooms /hour.
6--Therefore, the time required for both of them to paint the 1 room working together is 1 room/(A+B)/AB rooms/hour = AB/(A+B) = 5(3)/(5+3) = 15/8 hours = 1 hour-52.5 minutes.

Note - Generally speaking (if the derivation is not specifically required), if it takes one person A units of time and another person B units of time to complete a specific task working alone, the time it takes them both to complete the task working together is T = AB/(A + B), where AB/(A + B) is one half the harmonic mean of the individual times, A and B.

You might like to derive the equivalant expression involving 3 people working alone and together which results in T = ABC/(AB + AC + BC).
 
Methinks probably easier for students to "grasp" this by assuming one person does the work:
A = 8 hours, B= 5 hours, C = 4 hours
Step#1: 1/8 + 1/5 + 1/4 = 23/40
Now student can look at that as 1 person doing 23/40 of job in one hour:
how long to do the full job?
 
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