Two pipes A and B can separately fill a tank in 6 hours and...

Two pipes $A$ and $B$ can separately fill a tank in 6 hours and 8 hours, respectively. Both the pipes are opened together, but $1 \frac{1}{2}$ hours after the start, the pipe $A$ is tumed off. How much time will it take to fill the tank? (a) 5 hours (b) 6 hours (c) $4 \frac{1}{2}$ hours (d) $5 \frac{1}{2}$ hours

Two pipes $A$ and $B$ can separately fill a tank in 6 hours and 8 hours, respectively. Both the pipes are opened together, but $1 \frac{1}{2}$ hours after the start, the pipe $A$ is tumed off. How much time will it take to fill the tank?
(a) 5 hours
(b) 6 hours
(c) $4 \frac{1}{2}$ hours
(d) $5 \frac{1}{2}$ hours

Key Concepts

Rate of Work

The rate of work refers to the amount of work completed per unit of time. In problems involving work, such as filling a tank, each agent (or pipe) has a specific rate determined by how much of the task they can finish in one hour. This concept is fundamental to calculating how quickly a job can be completed under various conditions.

Combined Work Rate

When multiple agents work together simultaneously, their individual work rates can be added to determine their combined work rate. This concept is essential when two or more entities contribute concurrently to complete a single task, as it allows the overall time to completion to be calculated based on the sum of their contributions.

Sequential Work Process

Some problems require dividing the work into different stages, where the working conditions change over time. This involves calculating the amount of work completed in one phase and then analyzing the remaining work with a different rate. Understanding how to segment the problem into sequential steps is key to accurately determining the total time required for completion.

Fraction of Work Completed

Expressing work in terms of fractions enables the tracking of progress and helps to determine how much work remains after certain operations. By calculating the fraction of the task that has been completed in one time period, one can deduce the remaining fraction and use the respective work rate to estimate the additional time needed to finish the task.

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