Question

The first gardener can finish the job in 6 hours, and the second gardener can do the same job in 7 hours. How long it will take them to finish the same job, if they work together?

Answer 1

3 and 7/30 hours

Answer 2

If the first gardener can finish the job in 6 hours, it means that every hour he completes 1/6 of the job.

By the same logic, the second gardener completes 1/7 of the job per hour.

So, if they work together, they complete

`(1)/(6)+(1)/(7)=(7+6)/(42)=(13)/(42)`

of the job per hour.

So, after 42/13 of a hour, they'll complete the job. Since one hour is made of 60 minutes, 42/13 of a hour is

`(42)/(13)\cdot 60 \approx 194`

So, it will take them about 194 minutes to finish the job, i.e. about 3 hours and 14 minutes.