gaby236
If Jim Roller can paint a room in 3 hours while John Brush would take 5 hours, how long will they take if they work together?



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gaby236
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a;1/8 hour
b;8/15 hour
c; 7/8 hours

gaby236
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@RadEn

wio
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What class is this?

gaby236
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math

wio
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I know, but what level of math?

gaby236
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i need help

wio
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You need to make a system of equations.

wio
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Let, \(t\) be the time it takes to paint the room. \(r\) is the rate that Roller to paints it, \(b\) is the rate that Brush paints it.

wio
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We know that \[
3r = 5b
\]

wio
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We also know that \[
(r+b)t = 3r = 5b
\]

wio
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First solve for \(r\) in terms of \(b\) \[
3r=5b\implies r = \frac{5}{3}b
\]Now plug it into equation 2 \[
\left(\frac{5}{3}b+b\right)t=5b
\]

wio
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Then solve for \(t\).

RadEn
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shorcut way :
3*5/(3+5) = 15/8
long way :p
v1+v2 = x/3 + x/5 = 8x/15 = x/(15/8)
so, if they work together will take 15/8 hours

RadEn
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no correct options there