Jake, Lionel, and Wayne work as house painters for Paint Well Company. Jake can paint 1 room in t hours. Lionel can paint a room 2 hours faster than Jake can. Wayne can paint 2 rooms in 3 times the number of hours that Lionel takes to paint 1 room?

Question

Ethan Adkins · Accepted Answer

#12/7# hours to paint 1 room if they all work together

#color(red)("You have defined the work rate but not stated the number of rooms"# #color(red)("to be painted. I will work this out for 1 room and you will have to"# #color(red)("proportion this up (or down) for however many rooms are needed.")# For 1 room only: Jake #->1xxt " room hours"# Lional#-> 1xx(t-2)" room hours"# Wayne#->1xx(3(t-2))/2" room hours "larr" 2 rooms in "3(t-2)# '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("Determine the time for 1 room if they all work together")# #t+(t-2)+(3(t-2))/2=1# #t+t+3/2t-2-6/2=1# #7/2t=1+2+3# #t=(2xx6)/7 " hours"# #t=12/7" hours"larr" For 1 room"#

Jace Anderson · Answer

undefined Let $ t $ represent the time Jake takes to paint 1 room. Lionel takes $ t - 2 $ hours to paint 1 room. Wayne takes $ 3 \times (t - 2) $ hours to paint 1 room.