Working together, Sasha and Lorenzo can wash the dishes and 18 minutes. It's also washing the dishes alone, it will take him 15 minutes more than the amount of time it would take Lorenzo to wash the dishes alone. How long will it take Lorenzo to wash the dishes alone?

a. 45 minutes

b. 30 minutes

c. 9 minutes

d. none of these

Step-by-step explanation:

working together, Sasha and Lorenzo can wash the dishes and 18 minutes. Washing the dishes alone, it will take Sasha 15 minutes more than the amount of time it would take Lorenzo to wash the dishes alone. How long will it take Lorenzo to wash the dishes alone?

Sasha finishes the job alone in 18+15=33 minutes

L = time it takes Lorenzo alone

S = time it takes Sasha alone

Every minute,

Lorenzo will finish 1/L of the job

Sasha will finish 1/S of the job = 1/33

Together, they will finish 1/S+1/L of the job.

We know that it takes them 18 minutes to finish the job together, so we have

1/L + 1/S = 1/18

1/L + 1/33 = 1/18

1/L = 1/18 - 1/33 = 5/198

So

L = 198/5 = 39 3/5 minutes = 39.6 minutes

Answer: it will take Lorenzo 39.6 minutes to finish the dish-washing.