Question

2) Tim can finish painting his barn in 10 hours. It takes his wife JoAnn only 8 hours to do the same job.

If they work together, how long will it take them to complete the job?
3) Adan can do a piece of work in 3 days, Bernie in 4 days, and Cynthia in 6 days each working alone.
How long will it take them to do it working together?
4) A carpenter and his assistant can do a piece of work in 3 days. If the carpenter himself could do the
work alone in 5 days, how long would the assistant take to do the work alone?
5) A sink can be filled from the faucet in 5 minutes. It takes only 3 minutes to empty the sink when the
drain is open. If the sink is full and both the faucet and the drain are open, how long will it take to
empty the sink?
6) Of two inlet pipes, the smaller pipe takes 5 hours longer than the larger pipe to fill a pool. When
both pipes are open, the pool is filled in 6 hours. If only the larger pipe is open, how many hours are
required to fill the pool?
7) It takes John 16 minutes longer than Sally to mow the lawn. If they work together they can mow the
lawn in 15 minutes. How long will it take each to mow the lawn if they work alone?
8) Bill’s father can paint a room in 3 hours less than Bill can paint it. Working together they can
complete the job in 2 hours. How much time would each require working alone?
9) Two workers, a trainer and a trainee, working together can do a job in 3 hours. The trainer is 3 times
faster than the trainee to complete the same job. How long will it take the trainee to finish the same
job?
10) The faucet alone can fill the sink in 6 minutes, while it takes 8 minutes to empty it with the drain.
How long will it take to fill the sink?

Answer 1

Answer: For 2: 40/9 hours.

Explanation:

Tim can paint 1/10 of his barn in an hour.

JoAnn can paint 1/8 of the barn in an hour.

Now lets say if they work together they can paint 1/x of the barn in a hour.

Now we make an equation:

1/10 + 1/8 = 1/x

=>x/10 + x/8 = 1

=>x=40/9

If they work together, they can paint the barn in 40/9 hours.