Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, Then the tank will be filled in

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Find out how fast Pipes A, B, and C can fill or empty a tank. A takes 5 hours, B takes 6 hours, and C takes 12 hours. What happens when we open all three pipes together? Let’s solve the puzzle!

Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, Then the tank will be filled in

The time it takes to fill the tank when all three pipes are open is 3 9/17 hours.

Here’s the breakdown of the calculation:

1. Individual rates of the pipes:

   • Pipe A fills 1/5 of the tank per hour.
   • Pipe B fills 1/6 of the tank per hour.
   • Pipe C empties 1/12 of the tank per hour.

2. Net combined rate:

   • Net rate = (1/5) + (1/6) – (1/12) = 17/60 of the tank per hour.

3. Time to fill the tank:

   • Time = 1 / (net rate) = 60/17 hours = 3 9/17 hours.

Therefore, the correct answer is indeed 3 9/17 hours.

Rate and Time Problem in Mathematics

Here’s a breakdown of rate and time problems in mathematics:

Key Concepts:

• Rate: The speed or pace at which something occurs, usually expressed as a unit of quantity per unit of time (e.g., miles per hour, pages per minute, gallons per second).
• Time: The duration or length of a process or event, typically measured in units like hours, minutes, seconds, or days.
• Distance: The total amount of space covered during a movement, often measured in units like miles, kilometers, or meters.

Fundamental Formula:

• Distance = Rate × Time (D = RT)

Common Problem Types:

1. Finding the Rate:

   • If you know the distance and time, you can find the rate using: Rate = Distance / Time (R = D/T)
   • Example: A car travels 200 miles in 4 hours. What is its average speed?
     • Rate = 200 miles / 4 hours = 50 miles per hour

2. Finding the Time:

   • If you know the distance and rate, you can find the time using:Time = Distance / Rate (T = D/R)
   • Example: A train travels at 75 miles per hour for how long to cover 300 miles?
     • Time = 300 miles / 75 miles per hour = 4 hours

3. Finding the Distance:

   • If you know the rate and time, you can find the distance using the formula: Distance = Rate × Time (D = RT)
   • Example: A runner maintains a speed of 6 miles per hour for 2.5 hours. How far does she run?
     • Distance = 6 miles per hour × 2.5 hours = 15 miles

Units: Always ensure consistency in units when performing calculations.Direction: In motion problems, consider the direction of travel (e.g., upstream vs. downstream).Multiple Rates: Some problems involve multiple rates, requiring careful attention to each segment of a journey.

Strategies for Solving Rate and Time Problems:

1. Read the problem carefully to understand what is being asked and what information is given.
2. Identify the known and unknown quantities and assign variables if needed.
3. Choose the appropriate formula based on the information given and the unknown you’re trying to find.
4. Substitute the values into the formula and solve for the unknown.
5. Check your answer to make sure it makes sense in the context of the problem.

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Source: Math Hello Kitty
Categories: Math