Question

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?

Answer 1

Hint: To solve the given question, write all the data with respect to number of men’s, working hours and number of days, hence combine and compare all the data and solve for the data asked. i.e., 5 men work 6 hours a day in 20 days and 15 men work 8 hours a day in how many days represent this in mathematical form to solve easily.

Complete step-by-step solution:
Let us write the given data:
5 men = 6 hours a day = 20 days
15 men = 8 hours a day = how many days?
Instead of working with a number of men and the number of hours in a day, consider the number of 'man-hours' used.
As mentioned, 5 men working for 6 hours a day implies that:
\[5 \times 6 = 30\]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.
As mentioned, 15 men working for 8 hours a day implies that:
\[15 \times 8 = 120\] man-hours per day
To complete the task which requires 600 man-hours:
\[\dfrac{{600}}{{120}} = 5\]days.

Therefore, 15 men reap the field in 5 days.

Note: The key point to solve these type of rational equations sums is that we need to compare the data given with respect to the term asked and hence in the given question we can see that men are working hours a day to reap the field, we need to compare the given data and isolate the terms with respect to asked data. Hence by this method we can solve these sums.