# If 5 men working 6 hours a day can reap a field in 20 days, in how many days will 15 men reap the field if they work for 8 hours a day?

May 22, 2018

$5$ days

#### Explanation:

Instead of working with a number of men and the number of hours in a day, consider the number of 'man-hours' used.

$5$ men working for $6$ hours a day means:
$5 \times 6 = 30$ man-hours a day.

The entire task of reaping the field takes:
$30 \times 20 = 600$ man-hours

The question involves inverse proportion because if there are more men working and they work for more hours each day, then the task will be completed in fewer days.

$15$ men working for $8$ hours a day means:
$15 \times 8 = 120$ man-hours per day

To complete the task which requires $600$ man-hours:

$600 \div 120 = 5$ days