Question

You can complete one-half of a job in an hour. Your friend can complete one-third of the same job in an hour. How long will it take to complete the job if you work together? Write your answer as a decimal.

The job will take
hour(s).

Answer 1

1.2 hours

Explanation:

First note, rate and time are inverses of each other.

We need to find unit rate of each.

one-half job in 1 hour means

1 job in 1 * 2 = 2 hours

also

one-third job in 1 hour means

1 job in 1 * 3 = 3 hours

The rates are inverses, so we can say:

Rate 1 = 1/2

Rate 2 = 1/3

Working together, the rate would be:

1/2 + 1/3 = 5/6

The time it will take would be inverse of this, that would be:

`((5)/(6))^(-1)\\=(6)/(5)\\=1.2`

Working together, it will take 1.2 hours