Calculating Task Completion Time Together
This problem involves calculating the combined time taken by three individuals (A, B, and C) to complete a task when working together, given their individual completion times.
Individual Work Rates
First, determine the rate at which each person works. The rate is the amount of task completed per day. It's the inverse of the time taken to complete the task alone.
- A's time = 15 days. A's rate = $\frac{1}{15}$ task/day.
- B's time = 20 days. B's rate = $\frac{1}{20}$ task/day.
- C's time = 25 days. C's rate = $\frac{1}{25}$ task/day.
Combined Work Rate
When working together, their rates add up. Find the combined rate by summing their individual rates:
Combined Rate = A's Rate + B's Rate + C's Rate
Combined Rate = $\frac{1}{15} + \frac{1}{20} + \frac{1}{25}$
To add these fractions, find the Least Common Multiple (LCM) of the denominators (15, 20, 25). The LCM is 300.
Combined Rate = $\frac{1 \times 20}{15 \times 20} + \frac{1 \times 15}{20 \times 15} + \frac{1 \times 12}{25 \times 12}$
Combined Rate = $\frac{20}{300} + \frac{15}{300} + \frac{12}{300}$
Combined Rate = $\frac{20 + 15 + 12}{300} = \frac{47}{300}$ task/day.
Calculating Total Time Together
The time taken to complete the task together is the inverse of their combined rate:
Time Together = $\frac{1}{\text{Combined Rate}}$
Time Together = $\frac{1}{\frac{47}{300}}$
Time Together = $\frac{300}{47}$ days.
Therefore, A, B, and C can complete the task together in $\frac{300}{47}$ days.
Similar Questions
- A can lay railway track between two given stations in 22 days and B can do the same job in 10 days. With the help of C, they did the job in 2 days only. Then, C alone can do the job in
- Hema can do a certain piece of work in 30 days. Hema and Raji can together do the same work in 22 days, and Hema, Raji and Smitha can do the same work together in 15 days. In how many days can Hema and Smitha do the same work together?
- John, Johnny and Janardan can finish a task in a field in 6, 12, and 24 days, respectively. In how many days will they finish the task working together?
- Narendra finishes a job in 10 days. Amit completes the same job in 12 days. How many days will it take for both of them to finish the job while working together?
- Sita can clean a hotel in 20 days. Rita can clean the same hotel in 30 days. How many days will they take to clean the hotel together?
- A, B and C can complete a task in 36, 54 and 72 days respectively. Together they started the task but A left 8 days before the completion of the task while B left 12 days before the completion. The number of days for which C worked is:
- A alone can complete $\frac{2}{5}$ of a task in 12 days, while B alone can complete $\frac{3}{4}$ of the same task in 25 days. In how many days can they complete the task if they work together?
- A and B working alone can finish a task in 12 and 16 days respectively. In how many days can the task be finished if they work for one day each alternatively, and A begins the work?
- Reena and Jaya can complete a piece of work in 6 days and Jaya alone can complete it in 8 days. In how many days can Reena alone complete it?
- 12 people can sweep the floor in 4 days with 12 brooms. In how many days can 8 people sweep the floor with 8 brooms?
Important Questions from Time and Work
Mohan can do a piece of work in 10 days and Sohan in 15 days. They started working together, but after 3 days Mohan left the work . What time will Sohan take to finish the work?
A tank is filled in 8 hours by three taps A, B and C. The tap C is thrice as fast as B and B is twice as fast as A. How much time will pipe B alone take to fill the tank?
Had been one menless, then the number of days required to do a piece of work would have been one more. If the number of Man. Days required to complete the work is 56, how many workers were there?
A can do a piece of work in 16 hours, B and C can do it in 8 hours while A and C can do it 12 hours. How long will B alone take to do it?
- lf 12 men can do a work in 20 days, in how many days will the work be done by 15 men-
