Jenny leaves her house at 8:00 with some cupcakes for her daughter's birthday party at school. She jogs to the school at 15 miles per hour. Half an hour later, her wife Anna realizes that Jenny used peanut butter frosting because she forgot one of the kids in the class had a severe peanut allergy. Jenny doesn't have her cell phone, so Anna leaves the house driving at 45 miles her hour to catch Jenny and warn her. How long does Anna spend traveling in minutes? Think carefully first, then make a decision:
We know that the time that Anna spends traveling is 20 minutes less than Jenny's travel time: a = j - 20. We also know that the distance both people travel is equal, so their speeds times their travel times must be equal: 15j = 45a. Substituting the first equation into the second equation, we get 15j = 45(j - 20). Multiplying through the parentheses we get 15 j = 45j - 900. Subtracting 45 j from both sides, we get - 30j =  - 900. Dividing both sides by - 30, we get j = 30. Since Anna travels 20 minutes less than Jenny, she traveled 30 minutes - 20 minutes = 10 minutes. So, the answer is 10.