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.

15 hours
7.5 hours
3 hours
1.67 hours

1 answer

Let's denote George's work rate as \( g \) (in offices per hour) and Jerry's work rate as \( j \) (in offices per hour). We know from the problem that:

  1. Jerry paints twice as fast as George, so we can write: \[ j = 2g \]

  2. When working together, George and Jerry can paint the office in 5 hours, which means their combined work rate is: \[ g + j = \frac{1}{5} \text{ (offices per hour)} \]

Now, substituting \( j = 2g \) into the combined work rate equation gives us: \[ g + 2g = \frac{1}{5} \] \[ 3g = \frac{1}{5} \] \[ g = \frac{1}{15} \]

This means George's work rate is \( \frac{1}{15} \) offices per hour. To find out how long it takes George to paint the office by himself, we can take the reciprocal of his work rate: \[ \text{Time for George to paint the office} = \frac{1}{g} = \frac{1}{\frac{1}{15}} = 15 \text{ hours} \]

So, it would take George 15 hours to paint the office by himself. Thus, the answer is:

15 hours