Question

4. Kevin can clean a large aquarium tank in about 9 hours. When Kevin and Lara

work together, they can clean the tank in 6 hours. Write a rational equation that
could be used to determine how long it would take Lara to clean the tank if she
works by herself. You do not have to solve the equation. You may solve the
equation for extra credit.

Answer 1

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

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