Janice prepared 21 kilograms of dough after working 3 hours. How many hours did Janice work if she prepared 35 kilograms of dough, assuming the relationship is directly proportiona... Janice prepared 21 kilograms of dough after working 3 hours. How many hours did Janice work if she prepared 35 kilograms of dough, assuming the relationship is directly proportional?
Understand the Problem
The question is asking to find out how many hours Janice worked to prepare 35 kilograms of dough, given that she prepared 21 kilograms in 3 hours, assuming a direct proportional relationship between the amount of dough and the working hours.
Answer
5 hours
Answer for screen readers
Janice will take 5 hours to prepare 35 kilograms of dough.
Steps to Solve
- Find the rate of dough preparation
To find Janice's rate of dough preparation, divide the amount of dough she prepared by the time it took:
$$ \text{Rate} = \frac{\text{Amount of dough}}{\text{Time}} $$ $$ \text{Rate} = \frac{21 \text{ kg}}{3 \text{ hours}} = 7 \text{ kg/hour} $$
- Calculate the time to prepare 35 kg of dough
Now that we know her rate, we can calculate the time it will take to prepare 35 kg of dough. $$ \text{Time} = \frac{\text{Amount of dough}}{\text{Rate}} $$ $$ \text{Time} = \frac{35 \text{ kg}}{7 \text{ kg/hour}} = 5 \text{ hours} $$
Janice will take 5 hours to prepare 35 kilograms of dough.
More Information
This problem demonstrates a direct proportion: as the amount of dough increases, the time required also increases proportionally.
Tips
A common mistake is to set up the proportion incorrectly or to divide when you should multiply, or vice versa. For example, some might incorrectly calculate the time by multiplying the amount of dough by the rate instead of dividing. Always double-check the units to make sure the answer makes sense.
AI-generated content may contain errors. Please verify critical information
