Answer:
Part A
The rational equation that can be used to determine how long it would take Lara to clean the tank alone is; 6/9 + 6/x = 1
Part B
It would take Lara 18 hours to clean the tank if she works by herself
Step-by-step explanation:
Part A
The time it takes Kevin to clean an aquarium tank alone = 9 hours
The time it takes Kevin and Lara to clean the tank together = 6 hours
Let '1/x' represent Lara's cleaning rate, we have;
The time it would take Lara to clean 1 tank alone = 1/(1/x) = x
Kevin's cleaning rate, y = 1/9 tank per hour
The number of tanks, z = tank
The total time it takes both of them to clean the tank, t = 6 hours
Therefore, we get;
t × y + t × 1/x = z
When t = 6, y = 1/9, and z = 1, we get;
6 × (1/9) + 6·(1/x) = 1
Therefore, the rational equation that can be used to determine how long it would take Lara to clean the tank if she work by herself, '1/x', is given as follows;
6/9 + 6·(1/x) = 1
6/9 + 6/x = 1
Part B
Solving the rational equation gives;
1/x = (1 - 6/9)/6 = 1/18
∴ 1/x = 1/18)
∴ x = 18
The time it would take Lara to clean the tank if she worked by herself, x = 18 hours
