Let's denote the rate at which George can paint the office as \( G \) (in offices per hour). Since Jerry paints twice as fast as George, his rate will be \( 2G \).
When George and Jerry work together, their combined rate is: \[ G + 2G = 3G \] According to the problem, they can paint the office together in 5 hours. Therefore, their combined rate can also be expressed as: \[ \frac{1 \text{ office}}{5 \text{ hours}} = \frac{1}{5} \]
Setting the two expressions for their combined rate equal to each other: \[ 3G = \frac{1}{5} \] Now, we can solve for \( G \): \[ G = \frac{1}{5} \cdot \frac{1}{3} = \frac{1}{15} \]
This means George can paint \(\frac{1}{15}\) of the office in one hour. To find out how long it takes George to paint the whole office alone, we can take the reciprocal of his painting rate: \[ \text{Time for George} = \frac{1}{G} = \frac{1}{\frac{1}{15}} = 15 \text{ hours} \]
Thus, it would take George 15 hours to paint the office by himself.
The correct response is: 15 hours.
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