George and Jerry can paint the office in 5 hours working together. Since he is a professional painter, Jerry can paint twice as fast as George. Solve for how long it would take George to paint the office by himself.
Let's say George paints at a speed of x office/hour. Therefore, Jerry, being twice as fast, paints at a speed of 2x office/hour.
Working together, they have a combined speed of 3x office/hour.
From the problem, we know that they can paint the office in 5 hours. So, their combined speed is 1 office/5 hours, or 1/5 office/hour.
Setting the two expressions for speed equal to each other, we get 3x = 1/5.
Solving for x, we get x = 1/15 office/hour.
Therefore, it would take George 15 hours to paint the office by himself because his painting speed is 1/15 office/hour.
Let's assume that George's painting speed is represented by "G" (in units of work per hour). Since Jerry can paint twice as fast as George, Jerry's painting speed is 2G.
When George and Jerry work together, their combined painting speed is G + 2G = 3G (in units of work per hour).
We're given that George and Jerry can paint the office in 5 hours together. This means that in 1 hour, their combined speed completes 1/5th of the office work. Therefore, their combined painting speed is 3G = 1/5.
To find George's painting speed, we need to isolate G. We can do this by dividing both sides of the equation 3G = 1/5 by 3:
G = (1/5) / 3
G = 1/15
So George's painting speed is 1/15 of the office work per hour.
Since we want to find the time it takes for George to paint the office alone, we divide the total work (1) by George's painting speed (1/15):
Time taken by George to paint the office alone = 1 / (1/15)
Time taken by George to paint the office alone = 15
Therefore, it would take George 15 hours to paint the office by himself.
To solve this problem, let's assign variables to represent the time it takes for George and Jerry to complete the task individually.
Let's say George takes 'x' hours to paint the office by himself. Since Jerry is twice as fast as George, it would take him 'x/2' hours to complete the task alone.
When working together, George and Jerry can paint the office in 5 hours, so we can write the equation:
1/x + 1/(x/2) = 1/5
To simplify the equation, we need to find a common denominator:
2/(2x) + 1/(x/2) = 1/5
Now, combine the fractions:
4/(2x) + 2/x = 1/5
To eliminate the denominators, multiply every term by 10x:
4 * 10 + 2 * 10 = 2x
40 + 20 = 2x
60 = 2x
Divide both sides by 2:
x = 30
Therefore, George can paint the office by himself in 30 hours.