If 3 pipes can fill a tank in 4 hours, how long will it take for 5 such pipes to

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Question: If 3 pipes can fill a tank in 4 hours, how long will it take for 5 such pipes to fill the same tank?

Options:

Correct Answer: 2.4

Solution:

Rate of 3 pipes = 1/4 tank/hour. Rate of 1 pipe = 1/12 tank/hour. Rate of 5 pipes = 5/12 tank/hour. Time = 12/5 = 2.4 hours.

If 3 pipes can fill a tank in 4 hours, how long will it take for 5 such pipes to fill the same tank?

If 3 pipes can fill a tank in 4 hours, how long will it take for 5 such pipes to fill the same tank?

Step 1: Understand that 3 pipes can fill the tank in 4 hours.
Step 2: Calculate the rate at which 3 pipes fill the tank. Since they fill 1 tank in 4 hours, their rate is 1/4 tank per hour.
Step 3: Find the rate of 1 pipe. If 3 pipes fill at a rate of 1/4 tank per hour, then 1 pipe fills at a rate of (1/4) / 3 = 1/12 tank per hour.
Step 4: Calculate the rate of 5 pipes. If 1 pipe fills at a rate of 1/12 tank per hour, then 5 pipes fill at a rate of 5 * (1/12) = 5/12 tank per hour.
Step 5: Determine how long it takes for 5 pipes to fill the tank. Since they fill at a rate of 5/12 tank per hour, the time to fill 1 tank is 1 / (5/12) = 12/5 hours.
Step 6: Convert 12/5 hours to a decimal. 12/5 = 2.4 hours.

Rate of Work – Understanding how to calculate the rate at which multiple pipes can fill a tank and how to derive the time taken based on that rate.
Proportional Relationships – Recognizing the relationship between the number of pipes and the time taken to fill the tank.