Question

Working together, Sasha and Lorenzo can wash the dishes in 18 minutes. If Sasha washes 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 would it take Lorenzo to do the job alone

Answer 1

It takes Lorenzo 30 minutes to do the job alone

Explanation:

* Lets explain how to solve the problem

- Sasha and Lorenzo can wash the dishes in 18 minutes when they

are working together

- If Sasha washes the dishes alone, it will take him 15 minutes more

than the amount of time it would take Lorenzo to wash the

dishes alone

- Let t the time of Lorenzo to finish the job alone

∵ t is the time of Lorenzo to fish the job alone

∵ Sasha takes 15 minutes more than Lorenzo to finish the job alone

∴ The time of Sasha is t + 15

∵ They can finish the job together in 18 minutes

- Let the complete job is 1

∴
`(18)/(t)+(18)/(t+5)=1`

- To add two fraction with different denominators make L.C.M

∵ The L.C.M of t and t + 15 is t(t + 15)

∴
`(18)/(t)+(18)/(t+15)=(18(t+15)+18t)/(t(t+15))`

∴
`(18t+270+18t)/(t^(2)+15t)=1`

∴
`(36t+270)/(t^(2)+15t)=1`

- By using cross multiplication

∴ t² + 15t = 36t + 270

- Subtract 36t and 270 from both sides

∴ t² - 21t - 270 = 0

- Factorize it into two factors

∴ (t - 30)(t + 9) = 0

- Equate each bract by 0

∴ t - 30 = 0 ⇒ add 30 to both sides

∴ t = 30

- OR

∴ t + 9 = 0 ⇒ subtract 9 from both sides

∴ t = -9 ⇒ we will reject it because there is no time with - ve value

∴ t = 30 minutes

∵ t is the time of Lorenzo to fish the job

∴ It takes Lorenzo 30 minutes to do the job alone