# When working alone, painter W can paint a room in 2 hours, and working alone, painter X can paint ...

When working alone, painter W can paint a room in 2 hours, and working alone, painter X can paint the same room in h hours. When the two painters work together and independently, they can paint the room in 3/4 of an hour. What is the value of h?

## Answer/Solution

1[1/5]

### Steps/Work

Rate*Time=Work

Let Painter W's rate be W and Painter X's rate be X

R*T = Work

W * 2 = 1 (If the work done is same throughout the question then the work done can be taken as 1) => W = 1/2

X * h = 1 => X = 1/h

When they both work together then their rates get added up

Combined Rate = (W+X)

R*T = Work

(W+X) * 3/4 = 1

=> W+X = 4/3

=> 1/2 + 1/h = 4/3

=> 1/h = (8-3)/6 = 5/6

=> h = 6/5 = 1[1/5]

Answer B

Let Painter W's rate be W and Painter X's rate be X

R*T = Work

W * 2 = 1 (If the work done is same throughout the question then the work done can be taken as 1) => W = 1/2

X * h = 1 => X = 1/h

When they both work together then their rates get added up

Combined Rate = (W+X)

R*T = Work

(W+X) * 3/4 = 1

=> W+X = 4/3

=> 1/2 + 1/h = 4/3

=> 1/h = (8-3)/6 = 5/6

=> h = 6/5 = 1[1/5]

Answer B