Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Anita can clean a typical pool in 8 hours. Chao can clean a typical pool in 6 hours. How long should it take Anita and Chao working together to clean a typical pool? Show all your work. Leave your final answer as an integer or reduced fraction.
bot... answer the question
bot please answer the question
Sure! Anita can clean a typical pool in 8 hours. Chao can clean a typical pool in 6 hours. To find out how long it would take both of them working together to clean a typical pool, we can use the formula:
(time it takes working together) = (total work) / (combined rate of work)
The combined rate of work is the sum of their individual rates of work. We can find out their individual rates of work by taking the reciprocal of the time it takes each of them to clean the pool:
Anita's rate of work = 1/8 (because she can clean a pool in 8 hours)
Chao's rate of work = 1/6 (because he can clean a pool in 6 hours)
The combined rate of work is:
1/8 + 1/6 = 7/24
Now we can use the formula to find out how long it would take both of them working together:
(time it takes working together) = (total work) / (combined rate of work)
Since they need to clean 1 pool, the total work is 1. So:
(time it takes working together) = 1 / (7/24)
(time it takes working together) = 24/7
Therefore, it would take Anita and Chao about 3 and 3/7 hours, or approximately 3.43 hours, working together to clean a typical pool.
can you solve it just using numbers and equations
bot solve it the way I said
bot, can you please solve it just using numbers and equations
Sure! Let's use the following variables:
A = Anita's rate (in pools per hour)
C = Chao's rate (in pools per hour)
T = time it takes both of them working together (in hours)
W = the amount of work to be done, which is 1 pool
We know that Anita can clean a pool in 8 hours, so her rate is:
A = W / 8
Similarly, we know that Chao can clean a pool in 6 hours, so his rate is:
C = W / 6
When they work together, their rates add up, so:
A + C = W / T
Now we can substitute the values we found for A and C into this equation:
W / 8 + W / 6 = W / T
We can simplify this equation by finding a common denominator for the fractions on the left-hand side:
3W / 24 + 4W / 24 = W / T
7W / 24 = W / T
Finally, we can solve for T by cross-multiplying:
7W = 24W / T
T = 24 / 7
Therefore, it would take Anita and Chao approximately 3 and 3/7 hours, or approximately 3.43 hours, working together to clean a typical pool.
can you shorten that, still state what the variables mean
Of course! Let's use the following variables:
A = Anita's rate of work (pools per hour)
C = Chao's rate of work (pools per hour)
T = time it takes both of them working together (in hours)
W = the amount of work to be done, which is 1 pool
We know that:
A = W / 8 (because Anita can clean a pool in 8 hours)
C = W / 6 (because Chao can clean a pool in 6 hours)
When they work together, their rates add up, so:
A + C = W / T
Substituting the values we found for A and C, we get:
W/8 + W/6 = W/T
Finding a common denominator, we get:
3W/24 + 4W/24 = W/T
Simplifying, we get:
7W/24 = W/T
Cross-multiplying, we get:
T = 24/7
Therefore, it would take Anita and Chao approximately 3 and 3/7 hours, or approximately 3.43 hours, working together to clean a typical pool.
To find out how long it would take Anita and Chao working together to clean a typical pool, we can use the concept of rates.
First, let's find out how much of the job each person can complete in one hour.
Anita can clean 1/8 of the pool in one hour (since it takes her 8 hours to clean the whole pool). Similarly, Chao can clean 1/6 of the pool in one hour.
Now, let's add their individual rates to find out the combined rate at which they can clean the pool when working together.
1/8 + 1/6 = 3/24 + 4/24 = 7/24
So, when working together, Anita and Chao can clean 7/24 of the pool in one hour.
To find out how long it would take them to clean the entire pool, we can set up the equation:
(7/24) * t = 1
where t is the time it takes them to clean the pool (in hours) when working together.
To solve for t, we can multiply both sides of the equation by 24/7:
t = (1 * 24/7)
t = 24/7
Therefore, it would take Anita and Chao working together approximately 3 and 3/7 hours (or 3.43 hours) to clean a typical pool.