X.

12 + 13 = 1x. lint Solving, x = 115.

Therefore they together can do the work in $1\frac{1}{5}$ days.

1. A can do a piece of work in $3$ days, B in $5$ days, and C in $6$ days. How long will it take them to do it working together?

2. A can do a piece of work in $5$ days, B in $4$ days, and C in $3$ days. How long will it take them together to do the work?

3. A can do a piece of work in $2\frac{1}{2}$ days, B in $3\frac{1}{2}$ days, and C in $3\frac{3}{4}$ days. How long will it take them together to do the work?

4. A can do a piece of work in $10$ days, B in $12$ days; A and B together, with the help of C, can do the work in $4$ days. How long will it take C alone to do the work?

5. A and B together can mow a field in $10$ hours, A and C in $12$ hours, and A alone in $20$ hours. In what time can B and C together mow the field?

6. A and B together can build a wall in $12$ days, A and C in $15$ days, B and C in $20$ days. In what time can they build the wall if they all work together?

By working $2$ days each they build $\frac{1}{12}+\frac{1}{15}+\frac{1}{20}$ of it.

Exercise 59.

Ex. A cistern can be filled by three pipes in $15$, $20$, and $30$ hours, respectively. In what time will it be filled by all the pipes together?

lint Let x = the number of hours it will take all together. lint Then 1x = the part all together can fill in one hour. $\frac{1}{15}+\frac{1}{20}$ + 130 = the part all together can fill in one hour.

Therefore the pipes together can fill it in $6\frac{2}{3}$ hours.

1. A cistern can be filled by three pipes in $16$, $24$, and $32$ hours, respectively. In what time will it be filled by all the pipes together?

2. A tank can be filled by two pipes in $3$ hours and $4$ hours, respectively, and can be emptied by a third pipe in $6$ hours. In what time will the cistern be filled if the pipes are all running together?

3. A tank can be filled by three pipes in $1$ hour and $40$ minutes, $3$ hours and $20$ minutes, and $5$ hours, respectively. In what time will the tank be filled if all three pipes are running together?

4. A cistern can be filled by three pipes in $2\frac{1}{3}$ hours, $3\frac{1}{2}$ hours, and $4\frac{2}{3}$ hours, respectively. In what time will the cistern be filled if all the pipes are running together?

5. A cistern has three pipes. The first pipe will fill the cistern in $12$ hours, the second in $20$ hours, and all three pipes together will fill it in $6$ hours. How long will it take the third pipe alone to fill it?