Two pipes A and B can fill a tank in 16 hrs and 12 hrs respectively. The capacity of the tank is 240 liters. Both the pipes are opened simultaneously and closed after 2 hrs.

Two pipes A and B can fill a tank in 16 hrs and 12 hrs respectively. The capacity of the tank is 240 liters. Both the pipes are opened simultaneously and closed after 2 hrs. How much more water need to fill the tank?

After 2 hours, there are 170 liters of water still needed to fill the tank.

First, we need to find out how much water both pipes A and B can fill in 2 hours.

Pipe A fills 1/16 of the tank's capacity per hour. Pipe B fills 1/12 of the tank's capacity per hour.

So, in 2 hours:

• Pipe A fills 2 * (1/16) = 1/8 of the tank's capacity.
• Pipe B fills 2 * (1/12) = 1/6 of the tank's capacity.

Combined, both pipes fill: 1/8 + 1/6 = 3/24 + 4/24 = 7/24 of the tank's capacity in 2 hours.

Now, we need to find out how much of the tank's capacity is still left to be filled.

Initially, the tank needs 240 liters to be filled. In 2 hours, 7/24 of this capacity has been filled.

So, the remaining capacity to be filled is: 240 - 240 * (7/24) = 240 * (1 - 7/24) = 240 * (24/24 - 7/24) = 240 * (17/24) = 17 * 10 = 170

So, after 2 hours, there are 170 liters of water still needed to fill the tank.

Work and Time in Mathematics

Work and time problems in mathematics deal with determining the amount of work done or time required to complete a task, typically involving multiple entities working together or at different rates. These types of problems often involve the concept of rates, where the rate at which work is done or time is taken is measured in units of work per unit time (e.g., work per hour, work per day).

Here's a general approach to solving work and time problems:

1. Identify the Work to Be Done: Clearly understand the task at hand and what needs to be accomplished. This could involve completing a project, filling a tank, painting a wall, etc.

2. Determine the Rates of Work: Identify the rates at which each individual or entity can perform the work. This could be given in terms of work per unit time (e.g., items produced per hour, area painted per minute).

3. Set Up Equations: Use the rates of work to set up equations that represent the work done by each entity or individual. These equations often involve the concept that work done equals rate of work multiplied by time.

4. Solve the Equations: Solve the equations to find the unknowns, which could be the time taken to complete the task, the amount of work done by each entity, or any other relevant quantity.

5. Check Your Answer: Once you've found the solution, double-check to ensure that it makes sense in the context of the problem. For example, ensure that the time taken is reasonable and that the work done matches the requirements of the task.

Here's an example problem illustrating the concept:

Problem: If John can complete a job in 6 hours and Jane can complete the same job in 4 hours, how long will it take them to complete the job if they work together?

Solution: Let's denote the time taken by John to complete the job as t_J and the time taken by Jane to complete the job as t_Jane.

John's rate of work: 1/6 job per hour Jane's rate of work: 1/4 job per hour

When they work together, their rates of work add up:

Combined rate = 1/6 + 1/4 = 5/12 job per hour

Let t be the time it takes for them to complete the job together.

Using the formula Work = Rate × Time, we have:

Work done by John + Work done by Jane = Total work

(1/6)t + (1/4)t = 1

(5/12)t = 1

Solving for t, we get:

t = 12/5 hours = 2.4 hours

So, it will take John and Jane 2.4 hours to complete the job together.