Two painters can paint a room in 2 hours if they work together. The less experienced painter takes 4 hours more than the more experienced painter to finish the job. How long does it take for the less experienced painter to paint the room individually? Round to 2 decimal places.
L = M + 4 ... L - 4 = M
2/L + 2/M = 1 ... 2M + 2L = L M
2(2L - 4) = L^2 - 4L ... 0 = L^2 - 8L + 8
use quadratic formula to find L
Let's say the more experienced painter takes x hours to paint the room individually.
According to the given information, the less experienced painter takes 4 hours more than the more experienced painter to finish the job. So, the less experienced painter takes x + 4 hours to paint the room individually.
Now, we know that when they work together, they can paint the room in 2 hours.
Using the concept of work formula:
Combined work = Work rate of more experienced painter + Work rate of less experienced painter
The work formula can be expressed as:
1/2 = 1/x + 1/(x+4)
To solve this equation, we can multiply through by 2x(x+4) to eliminate the fractions:
x(x+4) + 2x = 2(x)(x+4)
x^2 + 4x + 2x = 2x^2 + 8x
x^2 + 6x = 2x^2 + 8x
Rearranging the terms, we get:
x^2 - 2x^2 + 8x - 6x = 0
Simplifying further, we get:
-x^2 + 2x = 0
Dividing through by -x, we get:
x - 2 = 0
Therefore, x = 2.
So, it takes the more experienced painter 2 hours to paint the room individually.
Now, to find the time taken by the less experienced painter to paint the room individually:
x + 4 = 2 + 4 = 6 hours.
Therefore, it takes the less experienced painter 6 hours to paint the room individually.
To solve this problem, let's assume that the less experienced painter takes x hours to paint the room individually.
First, we need to find the rates at which each painter can paint the room individually. The rate is defined as the inverse of the time it takes to complete the job. So, the more experienced painter's rate would be 1/2 room per hour, and the less experienced painter's rate would be 1/x room per hour.
According to the problem, the two painters can complete the job in 2 hours when they work together. To find their combined rate, we add up their individual rates:
1/2 + 1/x = 1/2
Now, let's solve this equation for x:
1/x = 1/2 - 1/2
1/x = 0
This equation tells us that the less experienced painter cannot complete the job alone since the rate is 0, which is not possible.
Therefore, it is not possible to determine how long it takes for the less experienced painter to paint the room individually because they cannot complete the job without the help of the more experienced painter.
rate of faster painter --- 1/x
rate of slower painter -- 1/(x+4)
combined rate = 1/x + 1/(x+4)
= (x+4 + x)/(x(x+4))
= (2x + 4)/(x^2 + 4)
1/[(2x + 4)/(x^2 + 4)] = 2
(x^2 + 4x)/(2x+4) = 2
x^2 + 4x = 4x + 8
x^2 = 8
x = √8 or appr 2.83 hrs