If A can complete a work in 10 days and B can complete the same work in 15 days, how long will it take for A and B to complete the work together?

To find the combined work rate, calculate the individual rates: A's rate = 1/10 work per day, B's rate = 1/15 work per day. Combined rate = 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6 work per day. Therefore, together they can complete the work in 6 days.

If A and B work together and finish a job in 12 hours, but A can do the job alone in 20 hours, how long can B do the job alone?

Let B's time to complete the job alone be x hours. A's rate = 1/20, B's rate = 1/x. Together, their rate = 1/12. Thus, 1/20 + 1/x = 1/12. Finding a common denominator and solving gives x = 30. Hence, B can complete the job alone in 30 hours.

A can complete a task in 24 days, and B can complete it in 18 days. If they start working together but A leaves after 6 days, how much work is left?

In 6 days, A completes 6/24 = 1/4 of the work, and B completes 6/18 = 1/3 of the work. Together, they complete 1/4 + 1/3 = 3/12 + 4/12 = 7/12 of the work. Hence, the remaining work is 1 - 7/12 = 5/12.

If a machine can produce a part in 5 minutes, and another machine can produce the same part in 3 minutes, how long will it take both machines to produce one part together?

The rate of the first machine is 1/5 parts per minute, and the second is 1/3 parts per minute. Combined rate = 1/5 + 1/3 = 3/15 + 5/15 = 8/15 parts per minute. Therefore, time to produce one part = 1 / (8/15) = 15/8 minutes or 1.875 minutes.

If C can complete a job in 8 hours, and D can complete it in 12 hours, how much time will they take to finish the job if C works alone for 3 hours and then D works alone for 2 hours?

C completes 3/8 of the job in 3 hours. D completes 2/12 = 1/6 of the job in 2 hours. Together, they complete 3/8 + 1/6 = 9/24 + 4/24 = 13/24 of the job. Therefore, the remaining work is 1 - 13/24 = 11/24. If C and D work together again, their combined rate = 1/8 + 1/12 = 5/24. Time to complete the remaining work = (11/24) / (5/24) = 11/5 hours or 2.2 hours.

If A can do a piece of work in 12 days, and B can do it in 15 days, how long will it take for both A and B to complete the work together?

A's rate = 1/12 and B's rate = 1/15. Combined rate = 1/12 + 1/15 = 5/60 + 4/60 = 9/60 = 3/20. Hence, they can complete the work together in 20/3 days or approximately 6.67 days.

If a group of 4 people can complete a task in 10 days, how long will it take for 6 people to complete the same task assuming they work at the same rate?

Work done = 4 people * 10 days = 40 person-days. For 6 people, time = 40 person-days / 6 people = 20/3 days or approximately 6.67 days.

A can do a work in 15 days, B can do it in 10 days. If both work together for 5 days, how much work is left?

A's rate = 1/15, B's rate = 1/10. Together, their rate = 1/15 + 1/10 = 1/6. In 5 days, they complete 5 * 1/6 = 5/6 of the work. Remaining work = 1 - 5/6 = 1/6.

If A alone can complete a work in 20 days and B alone can complete it in 30 days, how long will it take for both to complete it together?

A's rate = 1/20, B's rate = 1/30. Combined rate = 1/20 + 1/30 = 3/60 + 2/60 = 5/60. Therefore, they can complete the work together in 60/5 = 12 days.

A can do a work in 8 hours, B can do it in 12 hours. If they work together for 4 hours, how much work is left?

A's rate = 1/8, B's rate = 1/12. Combined rate = 1/8 + 1/12 = 3/24 + 2/24 = 5/24. In 4 hours, they complete 4 * (5/24) = 5/12 of the work. Remaining work = 1 - 5/12 = 7/12.

If A and B work together and finish a job in 12 hours, but A can do the job alone in 20 hours, how long can B do the job alone?

Let B's time to complete the job alone be x hours. A's rate = 1/20, B's rate = 1/x. Together, their rate = 1/12. Thus, 1/20 + 1/x = 1/12. Finding a common denominator and solving gives x = 30. Hence, B can complete the job alone in 30 hours.

A can complete a task in 24 days, and B can complete it in 18 days. If they start working together but A leaves after 6 days, how much work is left?

In 6 days, A completes 6/24 = 1/4 of the work, and B completes 6/18 = 1/3 of the work. Together, they complete 1/4 + 1/3 = 3/12 + 4/12 = 7/12 of the work. Hence, the remaining work is 1 - 7/12 = 5/12.