Question 404165
Justin's rate: {{{1/4}}} (1 room in 4 hrs)
Mark's rate: {{{1/3}}} (1 room in 3 hrs)
------------------------------
Their rate working together:
{{{ 1/4 + 1/3 = x/(3/4)}}} ({{{x}}} is the fraction of the room they cleaned in 3/4 hr)
{{{1/4 + 1/3 = (4x)/3}}}
Multiply other sides by {{{12}}}
{{{3 + 4 = 16x}}}
{{{16x = 7}}}
{{{x = 7/16}}} (fraction of room cleaned)
So, there is {{{1 - 7/16 = 9/16}}} of the room left to clean
Mark's rate is  {{{1/3}}}, so
{{{1/3 = (9/16)/t}}} ({{{t}}} is his time to clean {{{9/16}}} of a room)
Multiply both sides by {{{3t}}}
{{{t = 27/16}}}  hr
Note that {{{3/4 = 12/16}}}
It took them {{{12/16 + 27/16 = 39/16}}} hrs
That's 2 hrs + {{{(7/16)*60}}} = {{{26.25}}}
About 2 hrs and 26 min, unless I made a mistake