Question

pdf A group of college students are volunteering for Help the Homeless during their spring break. They are putting the finishing touches on a house they built. Working alone, Jorge can paint a certain room in 10 hours. Maria can paint the same room in 8 hours. Write an equation that can be used to find how long it will take them working together to paint the room. How many hours will it take them to paint the room

Answer 1

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