A painter can paint a racquetball court in 8 hours. His assistant needs an additional 2 hours to paint the same court working by himself. How long will it take both of them working together to paint the court.
painter's rate --> court/8
assistant's rate --> court/2
combined rate = court/8 + court/2 = 5court/8
time with combined rate = court/(5court/8)
=8/5 hours
To find out how long it will take both the painter and his assistant to paint the court together, we can use the concept of rates.
First, let's determine the rate at which the painter can paint the court per hour. We know that he can paint the entire court in 8 hours, so his painting rate is 1 court per 8 hours.
Next, let's determine the assistant's rate. We are told that the assistant takes an additional 2 hours to paint the court by himself, so his painting rate is 1 court per 10 hours.
Now, let's combine their rates to find the rate at which they can paint the court together. We can add their individual rates to get the combined rate:
1/8 + 1/10 = (5/40) + (4/40) = 9/40
This means that together, they can paint 9/40 of the court per hour.
To find out how long it will take both of them to paint the entire court, we can use the equation:
time = work / rate
Here, the work is 1 court, and the rate is 9/40 of the court per hour.
time = 1 / (9/40)
Now, let's simplify this expression:
time = 1 * (40/9)
time = 40/9
Therefore, it will take both the painter and his assistant approximately 4.44 hours (or 4 hours and 26 minutes) to paint the court together.