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

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

$\dfrac{1}{6}+\dfrac{1}{7}=\dfrac{7+6}{42}=\dfrac{13}{42}$

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

$\dfrac{42}{13}\cdot 60 \approx 194$

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