Math Destroyer test #2 Question 13 2014 edition

[ballerinacubana]

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James can paint a room in 4 hours, while Mike can paint the same in 5 hours. Working together, how many hours will take them to paint the room if James only works one hour.

I know that

J = 1/4hr -->if james worked 1/4 of the work
M = 1/5hr -->then Mike worked 3/4 of the work

Destroyer that Mike only needs to work (3/4)*5 = 15/4 = 3 3/4 hours and that is the answer but I do not understand the reasoning behind it. I hope you can help me with this problem

The answer is 3 3/4 hours

 

[DAT Destroyer]

Remember that: Rate = 1/time and job = rate x time
since James only worked only for 1 hour the job done is: J = (1/4)x1 = 1/4
3/4 of the job remains to be done. And now we work with Mike

3/4 = (1/5)xt solve for t and we get 15/4 = 3 3/4.

The longer way to do it is find how much of a job did James and Mike do in one hour.

J= (1/4 +1/5)x1 = 9/20
the remaining job is then 1 - 9/20 = 11/20
now mike will only work alone : 11/20 = (1/5)xt solve for t and get 55/20 = 11/4
And now we need to add the hour that both worked together : 11/4 + 1 = 15/4 = 3 3/4

Hope this helps! Good luck in your studies...

Nancy

 

[ballerinacubana]

Thank you Nancy. I understand now

 

[DAT Destroyer]

Thank you Nancy. I understand now

Glad I could help! take care..nancy

 

[moose786]

I'm confused by this problem, too. Mainly because of the wording: so first James works by himself on the paintjob for an hour. And then, Mike comes in after James leaves?

I interpreted it as both of them working together the first hour, then James leaving while Mike continued to paint until the job was done (which would be more complicated, and which I was having a hard time understanding how to do?)

Please clarify, if possible - idk if I'm approaching it correctly.

 

[Roy Williams]

I'm confused by this problem, too. Mainly because of the wording: so first James works by himself on the paintjob for an hour. And then, Mike comes in after James leaves?

I interpreted it as both of them working together the first hour, then James leaving while Mike continued to paint until the job was done (which would be more complicated, and which I was having a hard time understanding how to do?)

Please clarify, if possible - idk if I'm approaching it correctly.

It doesn't really matter when James works, just the fact that he works for an hour. So therefore you know that James painted 1/4 of the room since he can do a full room in 4 hours (therefore in a fourth of the time he does a fourth of the room). What's left for you to find out is how long it takes Mike to paint 3/4 of a room since that's all that is left.

The rest of this is easy now. We can just set up a proportion and cross multiply.

1/5 = (3/4)/x --> Solve for x = 15/4 = 3 3/4 hours

In words, this says: 1 room in 5 hours = 3/4 of a room in x hours.

Hope this helps! If it's still confusing let me know. When thinking about a problem logically, it is sometimes much easier to "work out" than plugging it into the formula. While that will get you the correct answer, I think this makes more sense and is quicker.

 

[moose786]

It doesn't really matter when James works, just the fact that he works for an hour. So therefore you know that James painted 1/4 of the room since he can do a full room in 4 hours (therefore in a fourth of the time he does a fourth of the room). What's left for you to find out is how long it takes Mike to paint 3/4 of a room since that's all that is left.

The rest of this is easy now. We can just set up a proportion and cross multiply.

1/5 = (3/4)/x --> Solve for x = 15/4 = 3 3/4 hours

In words, this says: 1 room in 5 hours = 3/4 of a room in x hours.

Hope this helps! If it's still confusing let me know. When thinking about a problem logically, it is sometimes much easier to "work out" than plugging it into the formula. While that will get you the correct answer, I think this makes more sense and is quicker.

I love you. This is exactly how I like to think of the problems, and couldn't for the life of me figure it out logically in my head. Your wording and step-by-step clarification made it much easier for me to grasp. Perhaps you should help update the Math Destroyer's solutions section with Nancy & Dr. Romano (not meaning to offend the Math Destroyer - it's amazing).