\nThis is a problem involving work and time, often solved using the concept of “Man-Days” or a formula relating work, men, and time.
\nLet W be the work done (number of mats woven), P be the number of persons, and D be the number of days. We can assume a constant rate of work per person per day.
\nThe total work done is proportional to the number of persons, the number of days, and the individual work rate (R).
\n$W \\propto P \\times D \\times R$
\nAssuming the work rate R per person per day is constant for both scenarios, we can write:
\n$W = k \\times P \\times D \\times R$
\nOr, more simply, the quantity $W \/ (P \\times D)$ is constant.
\n$\\frac{W_1}{P_1 \\times D_1} = \\frac{W_2}{P_2 \\times D_2}$<\/p>\nIn the first case:
\n$P_1 = 5$ persons
\n$D_1 = 8$ days
\n$W_1 = 160$ mats<\/p>\n
In the second case:
\n$P_2 = 8$ persons
\n$D_2 = 6$ days
\n$W_2 = ?$ mats<\/p>\n
Using the formula:
\n$\\frac{160}{5 \\times 8} = \\frac{W_2}{8 \\times 6}$
\n$\\frac{160}{40} = \\frac{W_2}{48}$
\n$4 = \\frac{W_2}{48}$
\n$W_2 = 4 \\times 48$
\n$W_2 = 192$<\/p>\n
So, 8 persons will weave 192 mats in 6 days.
\n<\/section>\n\nAssuming a constant individual work rate, the total work done is directly proportional to the number of workers and the time they work ($W \\propto P \\times D$). The relationship can be expressed as $\\frac{W_1}{P_1 D_1} = \\frac{W_2}{P_2 D_2}$.
\n<\/section>\n