Answer:
3 1/3 hours
Step-by-step explanation:
It takes Kevin 5 hours to clean the tank, but only 2 hours when he works together with Lara. You want to know how long it takes Lara to clean the tank working alone.
Rates
It is useful for "working together" problems to consider the rate of work being done in terms of projects per unit time. These rates add.
Kevin's rate: 1/5 tank/hour
Working together rate: 1/2 tank/hour
Sum of rates
Using ...
working together rate = Kevin's rate + Lara's rate
we find that ...
Lara's rate = working together rate - Kevin's rate
Lara's rate = (1/2 tank/hour) -(1/5 tank/hour) = 3/10 tank/hour
Project time
Then the time it takes for Lara working alone is ...
Time = (1 tank)/(Lara's rate) = (1 tank)/(3/10 tank/hour)
= 10/3 hours = 3 1/3 hours
It takes Lara 3 1/3 hours to clean the tank working by herself.
