Question

Mrs. Towle decided exactly one week (7 days) before Christmas that she wanted to buy a puppy for her husband. Her husband can build the fence working alone in 12 days, and with their normal working schedules, they could build the fence in 4 days working together. Will Mrs. Towle be able to get a puppy for her husband? Show work and explain your answer.

Answer 1

Mrs. Towle's husband will be able to build the fence before Christmas, and she will be able to get a puppy for him.

Explanation:

Mrs. Towle's husband can build the fence alone in 12 days and together with their normal working schedules in 4 days. Mrs.

Towle decided to get a puppy for her husband exactly 7 days before Christmas.

First, let's determine the rate at which Mrs.

Towle's husband and his wife can build the fence together per day:

If Mrs. Towle's husband can build the fence alone in 12 days, his daily rate is 1/12 of the fence.

If they can build the fence together in 4 days, their combined daily rate is 1/4 of the fence.

Now, let's calculate the portion of the fence they can build in 7 days:

Mrs. Towle's husband alone: 7 * (1/12) = 7/12 of the fence

Together with their normal working schedules: 7 * (1/4) = 7/4 of the fence

Since 7/4 is greater than the entire fence, they can complete the fence in 7 days.

Therefore, Mrs. Towle will be able to get a puppy for her husband before Christmas.

Thus, Mrs. Towle's husband will be able to build the fence before Christmas, and she will be able to get a puppy for him.