Question

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 1

Answer:

It take 12 hours for 2 lawnmowers to cut 6 acres of grass

Step-by-step explanation:

We are given that It takes 4 lawnmowers to cut 2 acres of grass in 2 hours.

Let $T_1 , M_1 and W_1$ denotes the time taken , No. of land mowers and Amount of grass respectively in case 1 .

$T_1=2 \\W_1=2\\M_1=4$

Now The amount of time varies directly with the amount of grass and inversely with the number of lawnmowers

Let $T_2 , M_2 and W_2$ denotes the time taken , No. of land mowers and Amount of grass respectively i case 2

$T_1=? \\W_1=6\\M_1=2$

So, $\frac{M_1 \times T_1}{W_1}=\frac{M_2 \times T_2}{W_2}$

Substitute the values

$\frac{4 \times 2}{2}=\frac{2 \times ?}{6}$

$\frac{4 \times 2 \times 6}{2 \times 2}=?$

$12=?$

Hence it take 12 hours for 2 lawnmowers to cut 6 acres of grass

Answer 2

Answer:

D. 12

Step-by-step explanation:

hope this helps :)