Question

A pipe fills a tank in 6 hours. Another pipe fills it in 8 hours. How long to fill the tank together?

• A. 3.43 hours
• B. 3.53 hours
• C. 3.63 hours
• D. 3.73 hours

Hint:

For combined work, add rates and take the reciprocal for time.

Answer 1

The Correct Option is A

To determine how long it takes for both pipes to fill the tank together, we start by calculating each pipe's rate of work:
The first pipe's rate is 1/6 of the tank per hour since it fills the tank in 6 hours.
The second pipe's rate is 1/8 of the tank per hour since it fills the tank in 8 hours.
When working together, the combined rate is (1/6 + 1/8) of the tank per hour.
To find this combined rate, calculate:
Combined Rate = 1/6 + 1/8
To add these fractions, find a common denominator. The least common multiple of 6 and 8 is 24.
Therefore:
(1/6 = 4/24) and (1/8 = 3/24)
Adding these, the combined rate is:
Combined Rate = 4/24 + 3/24 = 7/24 of the tank per hour.
This means that together, the pipes fill 7/24 of the tank per hour.
To find how long it takes to fill the tank, calculate the reciprocal of this rate:
Time = 24/7 hours
Performing the division gives:
Time ≈ 3.43 hours
Therefore, the correct answer is 3.43 hours.