A can do a piece of work in 20 days and B can do it in 15 days. How long will they take if both work together?

Answer 1

One good approach to this type of problem is to think of the two people working at certain speeds. If you simply add their speeds together, you'll get their combined rate of work:

A does 1 job per 20 days or a rate of 1/20 job per day.

B does 1 job per 15 days or a rate of 1/15 job per day.

Now add 1/20 + 1/15, using the usual methods for fractions to get 7/60 jobs per day. Convert this the number of days for one job by using a proportion 7 jobs/60 days = 1 job/x days. Solve with cross products to get:

7x = 60

x = 8.57 days

To give this answer a real-world test, consider that is more than twice the speed of A (the slower worker, so that's OK) but less than twice the speed of B, so this answer makes sense.