It takes 4 lawnmowers to cut 2 acres of grass in 2 hours. If the amount of time varies directly with the amount of grass and inversely with the number of lawnmowers, how many hours will it take 2 lawnmowers to cut 6 acres of grass?A. 3B. 4C. 8D. 12

Answer:It take 12 hours for 2 lawnmowers to cut 6 acres of grassStep-by-step explanation:We are given that It takes 4 lawnmowers to cut 2 acres of grass in 2 hours. Let [tex]T_1 , M_1 and W_1[/tex] denotes the time taken , No. of land mowers and Amount of grass respectively in case 1 .[tex]T_1=2 \\W_1=2\\M_1=4[/tex]Now The amount of time varies directly with the amount of grass and inversely with the number of lawnmowersLet [tex]T_2 , M_2 and W_2[/tex] denotes the time taken , No. of land mowers and Amount of grass respectively i case 2[tex]T_1=? \\W_1=6\\M_1=2[/tex]So, [tex]\frac{M_1 \times T_1}{W_1}=\frac{M_2 \times T_2}{W_2}[/tex]Substitute the values [tex]\frac{4 \times 2}{2}=\frac{2 \times ?}{6}[/tex][tex]\frac{4 \times 2 \times 6}{2 \times 2}=?[/tex][tex]12=?[/tex]Hence it take 12 hours for 2 lawnmowers to cut 6 acres of grass