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Algebraic Fractions question
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#1
So, my teacher gave me a question that goes like this:
A painter's apprentice takes 4 hours longer than a painter to pain a room on his own, but working together, they can paint the room in 1 and a half hours. How long does it take the painter to paint the room on his own?
I understand that this question involves setting up an equation involving algebraic fractions, but what would this equation be and how would you get there. From there I can solve it myself.
Thanks a lot guys
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A painter's apprentice takes 4 hours longer than a painter to pain a room on his own, but working together, they can paint the room in 1 and a half hours. How long does it take the painter to paint the room on his own?
I understand that this question involves setting up an equation involving algebraic fractions, but what would this equation be and how would you get there. From there I can solve it myself.
Thanks a lot guys
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kara1
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#2
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#2
start by writing down what you know in some algebraic form. assign letters to the painter/his apprentice and form some equations
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#3
(Original post by kara1)
start by writing down what you know in some algebraic form. assign letters to the painter/his apprentice and form some equations
start by writing down what you know in some algebraic form. assign letters to the painter/his apprentice and form some equations
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#4
(Original post by majmuh24)
That's the problem, I have that the painter time is x and apprentice time is x+4 but where would you go from there? I just don't know which equations to form
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That's the problem, I have that the painter time is x and apprentice time is x+4 but where would you go from there? I just don't know which equations to form
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#5
(Original post by StrangeBanana)
Start by writing down their work-rates. (i.e. rooms/hour), then find their combined work-rate. These questions are always kind of confusing.
Start by writing down their work-rates. (i.e. rooms/hour), then find their combined work-rate. These questions are always kind of confusing.
and it's simply a matter of solving from there? I'm normally pretty good at this kind of thing, it's just that this question confused me a little Posted from TSR Mobile
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#6
Focus on this thought: Ultimately what we are being asked is the speed with which the painter paints the room - hence how long it takes. From the info given that is what we need to calculate. Currently we only know the apprentice's speed and the combined speed.
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#7
(Original post by Old_Simon)
Focus on this thought: Ultimately what we are being asked is the speed with which the painter paints the room - hence how long it takes. From the info given that is what we need to calculate. Currently we only know the apprentice's speed and the combined speed.
Focus on this thought: Ultimately what we are being asked is the speed with which the painter paints the room - hence how long it takes. From the info given that is what we need to calculate. Currently we only know the apprentice's speed and the combined speed.
I think I've set up an equation above, so would that be right?
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#8
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#9
(Original post by MathsNerd1)
Wouldn't the two equations just be x+y=1.5, or 90 minutes but because you already know the painter apprentice takes 4 times longer than the painter, you've got x (the apprentice)= 4y, then just solve for y? Where y is the painter himself
Wouldn't the two equations just be x+y=1.5, or 90 minutes but because you already know the painter apprentice takes 4 times longer than the painter, you've got x (the apprentice)= 4y, then just solve for y? Where y is the painter himself
Also, he doesn't take 4 times longer, but 4 hours longer. Thanks for trying though
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#10
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#10
(Original post by majmuh24)
So they can do 1 room in 90 minutes. I think this gives
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So they can do 1 room in 90 minutes. I think this gives
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#11
(Original post by StrangeBanana)
But you have defined x and x + 4 as the lengths of time the painter and his apprentice take to paint a room, so when you do x over 90, you are doing a time divided by a time, which doesn't give you a "rate", which would be in Rooms per Time.
But you have defined x and x + 4 as the lengths of time the painter and his apprentice take to paint a room, so when you do x over 90, you are doing a time divided by a time, which doesn't give you a "rate", which would be in Rooms per Time.
I think I get it now, so it would be
[Latex]\dfrac{1}{x} + \dfrac{1}{x+4} = 90[\latex]
Thanks for the help though, I understand this type of question much more now (I always used to find stuff like this kind of confusing
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#12
(Original post by MathsNerd1)
I know, I realised the mistake as I sent it, what you should have then is just x+y=1.5, like before but say y=x+4 like you've suggested so you arrange for x to get you an answer? I'm pretty sure this is the correct route to take.
I know, I realised the mistake as I sent it, what you should have then is just x+y=1.5, like before but say y=x+4 like you've suggested so you arrange for x to get you an answer? I'm pretty sure this is the correct route to take.
You have to use algebraic fractions if that helps
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#13
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#13
(Original post by majmuh24)
Thanks for that, that explains a lot
I think I get it now, so it would be
[Latex]\dfrac{1}{x} + \dfrac{1}{x+4} = 90[\latex]
Thanks for the help though, I understand this type of question much more now (I always used to find stuff like this kind of confusing)
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Thanks for that, that explains a lot
I think I get it now, so it would be
[Latex]\dfrac{1}{x} + \dfrac{1}{x+4} = 90[\latex]
Thanks for the help though, I understand this type of question much more now (I always used to find stuff like this kind of confusing
)Posted from TSR Mobile
But it'd be equal to 3/2, btw, not 90 (hours, not minutes, as the x and x + 4 are in hours).
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#14
(Original post by StrangeBanana)
No problem.
But it'd be equal to 3/2, btw, not 90 (hours, not minutes, as the x and x + 4 are in hours).
No problem.
But it'd be equal to 3/2, btw, not 90 (hours, not minutes, as the x and x + 4 are in hours).
I always make stupid mistakes like this Anyway, are you doing the maths challenge next week?
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#15
(Original post by majmuh24)
Do you really know the apprentice's speed though? All the information you have is that it's 4 hours longer than the painter's time, so you don't have an actual value for it, only the combined time.
I think I've set up an equation above, so would that be right?
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Do you really know the apprentice's speed though? All the information you have is that it's 4 hours longer than the painter's time, so you don't have an actual value for it, only the combined time.
I think I've set up an equation above, so would that be right?
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Painters rate = joint rate - apprentices rate expressed as area per minute
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#16
(Original post by majmuh24)
Still no, cos this would give a negative time which is just nonsensical
You have to use algebraic fractions if that helps
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Still no, cos this would give a negative time which is just nonsensical
You have to use algebraic fractions if that helps
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#17
(Original post by majmuh24)
Ah right, thanks for that
I always make stupid mistakes like this
Anyway, are you doing the maths challenge next week?
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Ah right, thanks for that
I always make stupid mistakes like this Anyway, are you doing the maths challenge next week?
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The UKMT? Yeah, you?
Have you done it in previous years?
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#18
(Original post by StrangeBanana)
Me too, they're so annoying. xD
The UKMT? Yeah, you? Have you done it in previous years?
Me too, they're so annoying. xD
The UKMT? Yeah, you?
Have you done it in previous years?
Yeah, I've done it every year since Year 11 and did the Senior one this year, but that kind of failed since I only got Kangaroo
Have you done any prep yet?Posted from TSR Mobile
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#19
(Original post by Old_Simon)
We do not know the apprentices speed but we need to calculate it first.
Painters rate = joint rate - apprentices rate expressed as area per minute
We do not know the apprentices speed but we need to calculate it first.
Painters rate = joint rate - apprentices rate expressed as area per minute
Thanks for the help BTW
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#20
(Original post by majmuh24)
Yeah, I've done it every year since Year 11 and did the Senior one this year, but that kind of failed since I only got Kangaroo
Have you done any prep yet?
Yeah, I've done it every year since Year 11 and did the Senior one this year, but that kind of failed since I only got Kangaroo
Have you done any prep yet?
Y u do dis?And nah, I haven't really done any prep; might do some past questions tomorrow. The questions are always fun. ^^ And you?
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