Question

Chris and Melissa can clean a room together in 5 hours. Working alone Chris can clean the room in 1 hour less time than Melissa can.

Answer 1

How long does it take Melissa to clean the room alone ?

Answer 2

@jim_thompson5910

Answer 3

Rate that they work is inverse of time.
Together they work at a rate of 1/5 room per hour

Let c,m be the respective times
\[\frac{1}{c} + \frac{1}{m} = \frac{1}{5}\]
\[c = m-1\]
\[\rightarrow \frac{1}{m-1} + \frac{1}{m} = \frac{1}{5}\]
solve for m
\[\frac{m + (m-1)}{m(m-1)} = \frac{1}{5}\]
\[2m - 1 = \frac{1}{5} (m^2 - m)\]
\[m^2 - 11m +5 = 0\]
\[m = \frac{11 +\sqrt{101}}{2}\]

Answer 4

So how many hours ?

Answer 5

m hours