Chapter 3.7, Problem 37P

A child takes a nap averaging three hours and gets an average of 12 hours of sleep at night. Nap time and night time sleep can each vary by 30 minutes. What are the possible time lengths for the child’s nap and night time sleep?

To determine

The possible time lengths for the child`s nap and night time slap.

Answer to Problem 37P

The child`s nap time length is $2.5\text{hours}\le \text{nap}\text{time}\text{length}\le \text{3}\text{.5}\text{hours}$ .

The child`s night time slap length is $11.5\text{hours}\le \text{night}\text{slap}\text{time}\text{length}\le 12.\text{5}\text{hours}$ .

Explanation of Solution

Given:

Average time taken by child for nap = $3$ hours.

Average time taken by child for night sleep = $12$ hours.

Nap time and night time sleep can each vary by $30$ minutes.

Since, the night slap and nap time can vary up to $30$ minutes or it is $0.5\text{hours}$

Thus, the possible time length for child`s nap is $3\pm 0.5\text{hours}$ .

and the possible time length for child night slap is $\text{12±0}\text{.5}\text{hour}$ .

Hence, $2.5\text{hours}\le \text{nap}\text{time}\text{length}\le \text{3}\text{.5}\text{hours}$ .

Similarly, $11.5\text{hours}\le \text{night}\text{slap}\text{time}\text{length}\le 12.\text{5}\text{hours}$ .