Time And Work

To solve this problem, we first calculate the work done by A, B, and C. The work done by each individual per day is as follows:

• A can complete the work in 10 days, so A's work rate is of the work per day.
• B can complete the work in 12 days, so B's work rate is of the work per day.
• C can complete the work in 15 days, so C's work rate is of the work per day.

On every third day, A and C assist B. Thus, we need to calculate the work done in a 3-day cycle:

• Day 1: B works alone, completing of the work.
• Day 2: B works alone, completing another of the work.
• Day 3: A, B, and C work together, completing of the work.

Calculate the combined work done by A, B, and C on the third day:

So, in 3 days, the work completed is:

Thus, the work done in each cycle is . Find the total number of cycles needed to complete the work:

We need 1 unit of work completed:

To find the number of cycles n required, solve:

Solve for n:

This means 2.4 cycles are needed. Thus, B and A, C complete full cycles of 3 days each for 2 cycles (6 days), and only need a fraction of the next cycle.

Check how much work is done in 2 cycles:

2\times \frac{5}{12}=\frac{10}{12}=\frac{5}{6}

Work left after 2 cycles is:

Find the extra days needed to complete of the work. Since B alone works at a rate of per day:

Thus, completing the work takes the 6 days of full cycles plus 2 more days, summing up to a total of:

8 days

The correct answer is 8 .

A takes 10 days to complete the work, so A's work rate is of the work per day.
B takes 15 days to complete the work, so B's work rate is of the work per day.

When A and B work together, their combined work rate is:

This means A and B together can complete of the work per day.

They work together for 5 days, so the fraction of work completed by them in 5 days is:

Thus, of the work is completed. The remaining work is:

A now finishes the remaining of the work alone. Since A's work rate is of the work per day, the time A takes to complete the remaining work is:

Thus, the total time to complete the entire work is:

The whole work is completed in days.

• 1.
• 2.

To solve the problem, we need to determine when to turn off pipe B to fill the tank in exactly 20 minutes. The steps involve calculating the rates of the pipes and applying them to the time constraints.

Step 1: Calculate the rate of each pipe.

Pipe A can fill the tank in 32 minutes, so its rate is 1/32 tank per minute.

Pipe B can fill the tank in 48 minutes, so its rate is 1/48 tank per minute.

Step 2: Set up the equation based on the total operation time of 20 minutes.

Let be the time in minutes after which pipe B is turned off. In those minutes, both pipes work together. Therefore, for the next minutes, only pipe A is working.

The equation for the work done by both pipes in the initial minutes is:

The equation for the work done by pipe A in the remaining time is:

The sum of these equations equals 1 full tank:

Step 3: Solve the equation.

To solve this equation, find a common denominator for the fractions. The least common multiple of 32 and 48 is 96:

simplifies to:

Multiply every term by 96 to clear the denominators:

which simplifies to:

Conclusion: Pipe B should be turned off after 18 minutes for the tank to be filled in 20 minutes.

Given that two pipes A and B together can fill a tank in 40 minutes and pipe A is twice as fast as pipe B, we need to find out how long pipe A alone can fill the tank.

Let's assume the rate at which pipe B fills the tank is tanks per minute. Then, the rate at which pipe A fills the tank is tanks per minute because pipe A is twice as fast as pipe B.

Using the information that pipes A and B together can fill the tank in 40 minutes, we express their combined rate of filling tanks as .

The combined rate of 3x pipes per minute is enough to fill 1 tank in 40 minutes, so we have:

Solving for x:

Now that we know the rate for pipe B (x), let's use it to find the rate for pipe A, which is .

This means pipe A alone can fill the tank at a rate of tanks per minute, translating to filling the entire tank in 60 minutes or 1 hour.

Therefore, the correct answer is: 1 hour.