A contractor has 40 men to do a job in 60 days working 9 hours a day. How many more men are to be employed to finish the job in 48 days working 10 hours a day?

Step 1: Calculate the total work units for the initial conditions. The total work is proportional to the number of men, days, and hours per day. Let M_1 be the initial number of men, D_1 be the initial number of days, and H_1 be the initial hours per day. M_1 = 40 men D_1 = 60 days H_1 = 9 hours/day Total work units = M_1 × D_1 × H_1 Total work = 40 × 60 × 9 = 2400 × 9 = 21600 work units Step 2: Determine the number of men required for the new conditions. Let M_2 be the new number of men, D_2 be the new number of days, and H_2 be the new hours per day. D_2 = 48 days H_2 = 10 hours/day Since the total work remains the same: M_2 × D_2 × H_2 = Total work M_2 × 48 × 10 = 21600 M_2 × 480 = 21600 Step 3: Solve for M_2. M_2 = (21600)/(480) M_2 = (2160)/(48) M_2 = 45 men This is the total number of men needed to complete the job under the new conditions. Step 4: Calculate the number of more men needed. The contractor initially employed 40 men. The new requirement is 45 men. Number of more men needed = M_2 - M_1 More men = 45 - 40 = 5 men The contractor needs to employ 5 more men. --- Step 1: Simplify the left side of the equation. The given equation is: (3^3)/(9) = (1)/(3 - 2x) Calculate 3^3: 3^3 = 3 × 3 × 3 = 27 Substitute this value back into the left side: (27)/(9) = 3 Step 2: Rewrite the equation with the simplified left side. 3 = (1)/(3 - 2x) Step 3: Solve for x. Multiply both sides by (3 - 2x): 3(3 - 2x) = 1 Distribute the 3 on the left side: 9 - 6x = 1 Subtract 9 from both sides: -6x = 1 - 9 -6x = -8 Divide both sides by -6: x = (-8)/(-6) Simplify the fraction: x = (8)/(6) x = (4)/(3) The final answer for the word problem is 5 men. The final answer for the equation is x = (4)/(3). Send me the next one 📸