Question

Alvin and Resty can finish painting the room in two hours working together. Alvin can finish the same job in 3 hours less than Resty. How long will it take Resty to paint the room when he works alone?

Answer 1

Resty will take 6 hours to paint the room when he works alone.

Step-by-step explanation:

Let's assume that Resty takes x hours to paint the room when he works alone.

According to the information given in the question, Alvin can finish the job in 3 hours less than Resty. So, Alvin takes x - 3 hours to paint the room.

When Alvin and Resty work together, they can finish the job in 2 hours. This means that their combined work rate is 1/2 of the job per hour.

Using the concept of work rate, we can set up the equation:

1. Resty's work rate: 1/x (as he completes the job alone in x hours)
2. Alvin's work rate: 1/(x-3) (as he completes the job in x-3 hours)
3. Combined work rate: 1/2 (as they complete the job in 2 hours together)

Therefore, the equation is:

1/x + 1/(x-3) = 1/2

To solve this equation, we can multiply each term by 2x(x-3) to clear the fractions:

2(x-3) + 2x = x(x-3)

Expanding and simplifying:

2x - 6 + 2x = x^2 - 3x

4x - 6 = x^2 - 3x

Move all terms to one side of the equation:

x^2 - 7x + 6 = 0

Factoring the quadratic equation:

(x-6)(x-1) = 0

So, x-6=0 or x-1=0

Therefore, x=6 or x=1

Since we are looking for the time it takes Resty to paint the room alone, we take x=6.

Hence, it will take Resty 6 hours to paint the room when he works alone.