Questions: Camila went to the food pantry with her big sister last weekend. Their mom dropped them off at 1:00 and said, "I'll pick you up at 2:30." The girls spent 5/6 of an hour sorting canned goods, 2/3 of an hour cleaning up, and 1/2 an hour reading a book to some younger children. When they went out to meet their mom, she was already there. She said, "What have you been doing? I've been waiting for you!" How long had their mom been waiting for them? Show your thinking. Express your answer as a number of minutes and as a fraction of an hour.

Solution Steps

To find out how long Camila's mom had been waiting, we need to calculate the total time the girls spent on their activities and compare it to the time between when they were dropped off and picked up. First, sum the fractions of an hour they spent on each activity. Then, convert the total time spent into minutes and subtract it from the total time between drop-off and pick-up (1.5 hours or 90 minutes) to find the waiting time.

The time spent on each activity is as follows:

• Sorting canned goods: \( \frac{5}{6} \) hours
• Cleaning up: \( \frac{2}{3} \) hours
• Reading a book: \( \frac{1}{2} \) hours

To find the total time spent on activities, we sum these fractions: \[ \text{Total Activity Time} = \frac{5}{6} + \frac{2}{3} + \frac{1}{2} \]

The total time between when the girls were dropped off and when their mom was supposed to pick them up is: \[ \text{Total Time} = 1.5 \text{ hours} \]

To find out how long their mom had been waiting, we subtract the total activity time from the total time: \[ \text{Waiting Time} = \text{Total Time} - \text{Total Activity Time} \] Substituting the values: \[ \text{Waiting Time} = 1.5 - 2.0 = -0.5 \text{ hours} \]

The negative waiting time indicates that the girls took longer than the time their mom was waiting. Specifically, their mom had been waiting for \( 30 \) minutes less than the time they were supposed to be there.

Final Answer