Answer:
It takes Lorenzo 30 minutes to do the job alone
Step-by-step 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
∴ [tex]\frac{18}{t}+\frac{18}{t+5}=1[/tex]
- To add two fraction with different denominators make L.C.M
∵ The L.C.M of t and t + 15 is t(t + 15)
∴ [tex]\frac{18}{t}+\frac{18}{t+15}=\frac{18(t+15)+18t}{t(t+15)}[/tex]
∴ [tex]\frac{18t+270+18t}{t^{2}+15t}=1[/tex]
∴ [tex]\frac{36t+270}{t^{2}+15t}=1[/tex]
- 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
