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question：Professor Ali, a Middle Eastern Studies scholar, is preparing a lecture about the history of the Silk Road. To make the lecture engaging, he wants to include interesting facts and encourage his students to check the accuracy of these facts through simple calculations. He tells his students that the Silk Road was approximately 4,000 miles long. On his next slide, he shows that a camel caravan can travel about 20 miles per day. He asks his students to calculate how many days it would take for a caravan to travel the entire length of the Silk Road if they traveled without stopping. Later, he adds that if the caravan stops for rest every 5 days for 1 full day, how many total days will the journey take including the rest days?
answer：First, I need to determine the total travel time without any rest days by dividing the total distance by the daily travel distance.Next, I'll calculate the number of rest days required by dividing the travel days by the interval between rests and then multiplying by the number of rest days taken each time.Finally, I'll add the travel days and the rest days together to find the total duration of the journey, including the rest periods.
question：An amateur genealogist named Emily is just beginning her journey into discovering her family tree. She has learned that each generation back doubles the number of ancestors she has. Starting with her two parents, Emily wants to find out how many ancestors she has going back four generations from herself. Calculate the total number of ancestors Emily has in those four generations.
answer：First, I recognize that Emily starts with two direct ancestors: her mother and father.For each subsequent generation, the number of ancestors doubles. This means that in the first generation back, she has 2 ancestors, in the second generation, 4 ancestors, in the third generation, 8 ancestors, and in the fourth generation, 16 ancestors.To find the total number of ancestors across these four generations, I sum the ancestors from each generation: 2 + 4 + 8 + 16, which equals 30.Therefore, Emily has a total of 30 ancestors across four generations.
question：During high school, Jean-Leigh du Toit and her fellow field hockey player competed in 18 local competitions over the course of three years. In the first year, they played in 5 competitions and won 3 of them. In the second year, they participated in 7 competitions and won 4. In the final year, they played in 6 competitions. If they maintained the same winning ratio in the third year as their average winning ratio from the first two years, how many competitions did they win in the third year?
answer：First, I need to determine the total number of competitions Jean-Leigh du Toit and her team won in the first two years. In the first year, they won 3 out of 5 competitions, and in the second year, they won 4 out of 7 competitions. Adding these together gives a total of 7 wins.Next, I'll calculate the total number of competitions they participated in during the first two years. They played 5 competitions in the first year and 7 in the second year, totaling 12 competitions.To find the average winning ratio from the first two years, I'll divide the total wins by the total competitions: 7 wins divided by 12 competitions, which equals approximately 0.5833 or 58.33%.In the third year, they participated in 6 competitions. To maintain the same winning ratio, I'll multiply the number of competitions in the third year by the average winning ratio: 6 competitions multiplied by 0.5833, which equals approximately 3.5 wins.Since they can't win half a competition, I'll round this to the nearest whole number, which is 4 wins.
question：The funding agency officer has been allocated a budget of 150,000 to support the collider facility for the year. The facility requires 45,000 for maintenance, 30,000 for energy costs, and 20,000 for staffing. The officer also wants to allocate 15,000 for new equipment. After covering these expenses, the officer plans to distribute any remaining funds equally among 5 research projects. How much money will each research project receive?
answer：First, I need to determine the total budget allocated by the funding agency officer, which is 150,000.Next, I'll identify all the expenses that need to be covered:- Maintenance: 45,000- Energy costs: 30,000- Staffing: 20,000- New equipment: 15,000Adding these expenses together: 45,000 + 30,000 + 20,000 + 15,000 = 110,000.Now, I'll subtract the total expenses from the budget to find out how much money is left for the research projects: 150,000 - 110,000 = 40,000.Finally, I'll divide the remaining 40,000 equally among the 5 research projects: 40,000 ÷ 5 = 8,000 per project.
question：A sociologist is studying two rural communities, Village A and Village B, to understand the social impact of new agricultural policies. In Village A, there are 150 families, and each family has received 4 bags of seeds under the new policy. In Village B, there are 180 families, and each family has received 3 bags of seeds. How many more bags of seeds in total have been distributed in Village A compared to Village B?
answer：First, I need to determine the total number of seed bags distributed in each village.For Village A, there are 150 families, and each family received 4 bags of seeds. So, the total number of bags in Village A is 150 multiplied by 4, which equals 600 bags.In Village B, there are 180 families, and each family received 3 bags of seeds. Therefore, the total number of bags in Village B is 180 multiplied by 3, which equals 540 bags.To find out how many more bags were distributed in Village A compared to Village B, I subtract the total bags in Village B from the total bags in Village A: 600 minus 540 equals 60 bags.
question：Dr. Quantum, a renowned theoretical physicist, has published 12 papers on quantum mechanics and 8 papers on string theory. Each quantum mechanics paper took her 3 weeks to write, while each string theory paper took her 5 weeks to write. If Dr. Quantum decides to take a well-deserved vacation for the same number of weeks it took her to write all her papers, how many weeks will her vacation last?
answer：First, I need to determine the total time Dr. Quantum spent writing her papers. She has written 12 papers on quantum mechanics, and each took her 3 weeks to write. So, the time spent on quantum mechanics papers is 12 multiplied by 3, which equals 36 weeks.Next, she has written 8 papers on string theory, and each of those took her 5 weeks to write. Therefore, the time spent on string theory papers is 8 multiplied by 5, which equals 40 weeks.To find the total time spent writing all the papers, I add the time spent on quantum mechanics and string theory together: 36 weeks plus 40 weeks equals 76 weeks.Since Dr. Quantum plans to take a vacation for the same number of weeks she spent writing, her vacation will last 76 weeks.