Answer:
the equation would be
t = tM/(1+tM/tJ) = tM*tJ/(tM+tJ)
and the time required for both to paint the room when they work together is t= 4.44 hours
Step-by-step explanation:
For Jorge
Painted surface of the room = velocity of painting of Jorge * time required for Jorge to paint the room
For Maria
Painted surface of the room = velocity of painting of Maria* time required for Maria to paint the room
then
velocity of painting of Jorge * time required for Jorge to paint the room= velocity of painting of Maria* time required for Maria to paint the room
or
velocity of painting of Jorge =velocity of painting of Maria* time required for Maria to paint the room/time required for Jorge to paint the room ) = velocity of painting of Maria* (8 hours/10 hours)= 0.8*velocity of painting of Maria
thus Jorge paints 20% slower than Maria
Then if they will paint together i will assign them different portions of the room so they do not disturb each other for painting ( work in parallel) and assign this portions so they end at the same time ( so there is no dead time and i minimise the time required)
then
Surface painted of Jorge = velocity of painting of Jorge * time required for both to paint the room
Surface painted of Maria = velocity of painting of Maria * time required for both to paint the room
such that
Surface painted of Jorge + Surface painted of Maria= Painted surface of the room
replacing the equations
velocity of painting of Jorge * time required for both to paint the room + velocity of painting of Maria * time required for both to paint the room = velocity of painting of Maria* time required for Maria to paint the room
since velocity of painting of Jorge= 0.8*velocity of painting of Maria
0.8*velocity of painting of Maria * time required for both to paint the room + velocity of painting of Maria * time required for both to paint the room = velocity of painting of Maria* time required for Maria to paint the room
thus
1.8* time required for both to paint the room= time required for Maria to paint the room
time required for both to paint the room = time required for Maria to paint the room/1.8 = 8 hours/ 1.8 = 4.44 hours
the equation would be
t = tM/(1+tM/tJ) = tM*tJ/(tM+tJ)
or
1/t= 1/tM + 1/tJ (work in parallel)
where
t = time required for both to paint the room
tM = time required for Maria to paint the room
tJ = time required for Jorge to paint the room
