Question

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?
Can you put it in steps, so I understand it?

Answer 1

1) we calculate the portion of pool cleaned by Anita in a hour.
1 pool cleaned-----------------8 hour
x-----------------------------------1 hour

x=(1 pool cleaned * 1 hour) / 8 hour=1/8 portion cleaned.

2) we calculate the portion of pool cleaned by Chao  in a hour.
1 pool cleaned-----------------6 hour
x-----------------------------------1 hour

x=(1 pool cleaned * 1 hour) / 6 hour=1/6 portion cleaned.

3) we can suggest this equation:
x=number of hour

x(1/8+1/6)=1

(number of hour)*(portion of pool cleaned by Anita in a hour + portion of pool cleaned by Chao in a hour)=1 pool cleaned.

4) we solve this equation:
x(1/8 + 1/6 )=1

1/8+1/6=(3+4)/24=7/24
least common multiple (8,6)=24

x(7/24)=1
x=(1*24)/7
x=24/7≈3.43     (3 hours,  25 minutes, 43 seconds)

Answer:together they cleaned the pool in 3 hours, 25 minutes and 43 seconds.