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Question 931695: 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.
a. Write an expression to represent the number of rooms per hour that each person can paint.
b. Write an expression to represent the total number of rooms per hour that Jake, Lionel, and Wayne can paint together.
c. If Jake can paint 1 room in 8 hours, find the rate, in terms of number of rooms per hour, at which Jake, Lionel, and Wayne can paint working together.
d. Wayne gets sick and is unable to work. What is the rate, in rooms per hour, at which Jake and Lionel can paint together? Work with the expression you wrote in part b.
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! a. Jake paints 1 room in t hours.
Then Jake paints at the rate of 1/t rooms/hr
Lionel paints 1 room in t-2 hours.
Lionel paints at the rate of 1/(t-2) rooms/hr
Wayne paints 2 rooms in 3(t-2) hours.
Wayne paints at the rate of 2/3(t-2) rooms/hour
b. Together, Jake, Lionel and Wayne can paint
1/t + 1/(t-2) + 2/3(t-2) multiply numerator and denominator of each term by 3t(t-2)
(3(t-2)+3t+2t)/3t(t-2)=(3t-6+5t)/3t(t-2)=(8t-6)/3t(t-2)
c.If t=8, then we have from b.:
(8*8-6)/3*8(8-2)=58/144= (29/72) rooms/hour
d. 1/t + 1/(t-2) multiply numerator and denominator by t(t-2)
((t-2)+t)/t(t-2)(2t-2)/t(t-2) rooms/hour
Hope this helps----ptaylor
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