Dan and don can clean a pen together in 45minutes. Dan can clean the pen alone in an hour. How long does it take for Don to clean the pen alone?
Cant even figure out how to properly set up this equation let alone solve..

Question

Dan and don can clean a pen together in 45minutes. Dan can clean the pen alone in an hour. How long does it take for Don to clean the pen alone?
Cant even figure out how to properly set up this equation let alone solve..

anonymous · Answer

anyone?

kropot72 · Answer

Let x be the number of hours for Don to clean the pen alone. Then in 1 hour the proportion of pen cleaning by Dan and Don working together will be
$$1+\frac{1}{x}=\frac{x+1}{x}$$
But this proportion of pen cleaning is the inverse of 3/4. Therefore
$$\frac{x+1}{x}=\frac{4}{3}$$
4x = 3x + 3
Now just solve for x

raden · Answer

alternative :
we convert the hour's unit to minute, we knowed 1 hour = 60 minutes

The time if do together = (Dan's time * Don's time)/(Dan's time+Dons time)
45 = 60x/(60+x)    (i assumed x is Dons time if do alone)
simplied be 
3 = 4x/(60+x) or
3(60+x) = 4x
3x + 180 = 4x
now, find the value of x (in minute)