Blake and Luke can paint a room in 15 hours. Luke can paint the room by himself in 25 hours.
How long does it take Blake to paint?
1/B + 1/25 = 1/15
To find out how long it takes Blake to paint the room, we can first calculate the rate at which Blake and Luke paint together:
Let's assume that Blake's rate is B rooms per hour, and Luke's rate is L rooms per hour.
According to the given information, Blake and Luke can paint a room together in 15 hours. So their combined rate is 1 room per 15 hours.
So the equation becomes:
B + L = 1/15 ---(1)
We also know that Luke can paint the room by himself in 25 hours. So his rate is 1 room per 25 hours.
So the equation becomes:
L = 1/25 ---(2)
Now we can substitute equation (2) into equation (1) and solve for B:
B + 1/25 = 1/15
Multiply both sides of the equation by 25 to eliminate the fraction:
25B + 1 = 25/15
25B = 25/15 - 1
25B = 5/15
B = (5/15)/25
B = 1/75
Therefore, it would take Blake 75 hours to paint the room by himself.
To find out how long it takes Blake to paint the room, we need to determine his painting rate. Let's assume that Blake's painting rate is represented by x.
Given that Blake and Luke can paint the room together in 15 hours, we can write the equation as follows:
1/x + 1/25 = 1/15
To solve this equation and find the value of x, we can follow these steps:
Step 1: Multiply both sides of the equation by the LCD (Least Common Denominator) of x, 25, and 15, which is 375.
15*x + 375/25 = 375/15
Step 2: Simplify the equation.
15*x + 15*15 = 375
Step 3: Combine like terms.
15*x + 225 = 375
Step 4: Subtract 225 from both sides of the equation.
15*x = 375 - 225
15*x = 150
Step 5: Divide both sides of the equation by 15 to solve for x.
x = 150/15
x = 10
Therefore, Blake's painting rate is 10. This means that it would take Blake 10 hours to paint the room by himself.