Chapter 5.1, Problem 40PPS

To determine

Find how much time can Kono volunteer this week.

Answer to Problem 40PPS

At most 19 hours and 25 minutes more this week.

Explanation of Solution

Given:

Kono knows that he can only volunteer up to 25 hours per week. If he has volunteered for the times recorded at the right.

Shelter − 3 h 15 min and Kitchen − 2 h 20 min.

Concept Used:

Let t = the amount of time in hours, left in the week for Kono to volunteer.

Shelter − 3 h 15 min and kitchen − 2 h 30 min.

So Shelter + Kitchen = 3h 15 min + 2 h 20 min = 5 h 35 min

  $5\text{hr}35\min =5+\frac{35}{60}=5\frac{7}{12}\text{hr}$ [1 hour = 60 min]

In equality: $5\frac{7}{12}+t\le 25$

Calculation:

Let t = the amount of time in hours, left in the week for Kono to volunteer.

Shelter + Kitchen = 3h 15 min + 2 h 20 min = 5 h 35 min

  $5\text{hr}35\min =5+\frac{35}{60}=5\frac{7}{12}\text{hr}$ [ 1 hour = 60 min]

In equality: $5\frac{7}{12}+t\le 25$

Solve for t :

  $\begin{array}{l}5\frac{7}{12}+t\le 25\\ 5\frac{7}{12}-5\frac{7}{12}+t\le 25-5\frac{7}{12}\text{[}\text{Subtract}5\frac{7}{12}\text{from}\text{both}\text{sides}\text{]}\\ t\le 19\frac{5}{12}\end{array}$

  $19\frac{5}{12}\text{hr}=19+\frac{5}{12}\text{hr}=19\text{hr}+\frac{5}{12}·60\min =19\text{hr}25\min$ [ 1 hour = 60 min]

So, Kono can volunteer at most 19 hours and 25 minutes more this week.

Thus, Kono can volunteer at most 19 hours and 25 minutes more this week.