Last Updated on May 10, 2023
GMAT OFFICIAL GUIDE PS
Solution:
To solve, we want to use the combined worker formula:
work of pump 1 + work of pump 2 = total work completed
Let’s start by determining the rates of both pumps.
We are given that one pump fills an empty tank to ½ of its capacity in 3 hours.
rate = work/time
rate = (½)/3 = 1/6
We are given that a second pump fills the same tank to 2/3 of capacity in 6 hours.
rate = (2/3)/6
rate = 1/9
We need to determine how many hours it will take both machines working together to fill the empty tank to capacity. Since both machines are working together, we can say that they both work for h hours. Using the formula work = rate x time, we know:
work of pump 1 = (1/6)h
work of pump 2 = (1/9)h
We can plug this information into the combined worker formula to determine h. Remember, we must use a value of 1 for total work since 1 job is completed.
(1/6)h + (1/9)h = 1
Multiplying the equation by 18 (to clear the equation of fractions) we obtain:
3h + 2h = 18
5h = 18
h = 18/5 = 3 3/5 = 3.6
Answer: B
