Selma's class is making care packages to give to victims of a natural disaster. Selma packs one box in 5 minutes and has already packed 12 boxes. Her friend Trudy packs one box in... Selma's class is making care packages to give to victims of a natural disaster. Selma packs one box in 5 minutes and has already packed 12 boxes. Her friend Trudy packs one box in 7 minutes and has already packed 18 boxes. How many more minutes does each need to work in order to have packed the same number of boxes?
Understand the Problem
The question is asking how many more minutes Selma and Trudy need to work in order to have packed the same number of boxes. We will calculate how many boxes each has packed already, their packing rates, and then determine the time required for them to equalize their total boxes packed.
Answer
Both need approximately $105.07$ more minutes to have packed the same number of boxes.
Answer for screen readers
Both Selma and Trudy need approximately ( 105.07 ) more minutes to have packed the same number of boxes.
Steps to Solve
- Determine Selma's packing rate
Selma packs 1 box in 5 minutes, which means her packing rate is: $$ \text{Selma's rate} = \frac{1 \text{ box}}{5 \text{ minutes}} = 0.2 \text{ boxes per minute} $$
- Calculate total boxes packed by Selma
Selma has already packed 12 boxes.
- Determine Trudy's packing rate
Trudy packs 1 box in 7 minutes, so her packing rate is: $$ \text{Trudy's rate} = \frac{1 \text{ box}}{7 \text{ minutes}} \approx 0.1429 \text{ boxes per minute} $$
- Calculate total boxes packed by Trudy
Trudy has already packed 18 boxes.
- Set up the equation for time
Let ( t ) be the time in minutes that both need to pack more boxes. After ( t ) minutes, Selma will have packed ( 12 + 0.2t ) boxes and Trudy will have packed ( 18 + 0.1429t ) boxes. We want them to be equal: $$ 12 + 0.2t = 18 + 0.1429t $$
- Solve for ( t )
Rearranging the equation gives: $$ 0.2t - 0.1429t = 18 - 12 $$ $$ 0.0571t = 6 $$
Dividing both sides by 0.0571: $$ t \approx \frac{6}{0.0571} \approx 105.07 \text{ minutes} $$
- Calculate individual minutes required to reach equality
Both need to work for approximately 105 more minutes.
Both Selma and Trudy need approximately ( 105.07 ) more minutes to have packed the same number of boxes.
More Information
Selma's and Trudy's initial packing progress varies, leading to different total times needed. This illustrates the importance of rates in problem-solving.
Tips
- Misinterpreting the rates can lead to incorrect equality setup.
- Forgetting to include the number of boxes already packed in the total calculations can also lead to errors.
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