Answer:
Example 1:
A tank can be filled by pipe A in 3 hours and by pipe B in 5 hours. When the tank is full, it can be drained by pipe C in 4 hours. if the tank is initially empty and all three pipes are open, how many hours will it take to fill up the tank?
Solution:
Step 1: Assign variables:
Let x = time taken to fill up the tank
Step 2: Use the formula:
Since pipe C drains the water it is subtracted.
1/3+1/5-1/4=1/x
Step 3: Solve the equation
The LCM of 3, 4 and 5 is 60
Multiply both sides with 60
solve the eqn
Answer: The time taken to fill the tank is 3 9/17 hours.
Work Problem: Pumps draining a tank
Example:
A swimming pool can be emptied in 6 hours using a 10-horsepower pump along with a 6-horsepower pump. The 6-horsepower pump requires 5 hours more than the 10-horsepower pump to empty the pool when working by itself.
How long will it take to empty the pool using just the 10-horsepower pump?
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Cooperative Work Word Problems (Time to Finish)
Examples:
1. Pump A can empty a pool in 20 hours and pump B can empty it in 24 hours. Working together, how long will it take to empty the pool?
2. A painter can paint a building in 15 days and a coworker can do the same job in 10 days. If the first painter starts and 3 days later the coworker joins in to help finish the job, how many days doe it take to paint the building?
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Rates of Performing Work Problems
Example:
It takes 12 hours to fill a water tank. It takes 16 hours to drain the same water tank. How long will it take to fill the tank if the drain is left open?
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Explanation: