Question

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.

e. The Paint Well Company hires Donald as a replacement for Wayne. Donald takes twice the time taken by Lionel to paint 1 room. Write an expression to represent the total number of rooms that Jake, Lionel, and Donald can paint together in 1 hour.

f. Find the number of rooms per hour that Jake, Lionel, and Donald can paint working together if t is 6 hours.

g. Compare the rate at which Jake, Lionel, and Donald paint (part f) with the rate at which Jake, Lionel, and Wayne paint (part c). Determine whether the new rate is faster or slower and by how much.

h. Apply the rate you computed in part f to determine how long it would take Jake, Lionel, and Donald to paint 6 rooms in a house.

Answer 1

Hours to paint one room 
Jake: t hours 
Lionel: t-2 hours 
Wayne: (1.5)(t-2) hours 

Now who is Donald? 

Shall we assume that by "Donald" you meant "Wayne"? 

If t is 6 hours, then the hours to paint one room is 
Jake: 6 hours 
Lionel: 4 hours 
Wayne: 6 hours 
This means that in one hour: 
Jake can paint 1/6 of a room, 
Lionel can paint 1/4 of a room, 
Wayne can paint 1/6 of a room. 
Added together, the three of them can paint (1/6 + 1/4 + 1/6) = 7/12 of a room in one hour.