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

D. 12

Explanation:

hope this helps :)

Answer 2

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

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,
`(M_1 * T_1)/(W_1)=(M_2 * T_2)/(W_2)`

Substitute the values

`(4 * 2)/(2)=(2 * ?)/(6)`

`(4 * 2 * 6)/(2 * 2)=?`

`12=?`

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