Appearance
question：An investor is planning to install a solar-powered irrigation system on a farm. The cost of installing the system is 3,000 per acre. The investor has a budget of 15,000. Each acre equipped with the system can save the farm 500 per year in water costs. How many acres can the investor install the solar-powered irrigation system on with their budget, and what will be the total annual savings in water costs for those acres?
answer：First, I need to determine how many acres the investor can install the solar-powered irrigation system on with their 15,000 budget. Since the cost per acre is 3,000, I'll divide the total budget by the cost per acre to find the number of acres.Next, I'll calculate the total annual savings in water costs. Each acre equipped with the system saves 500 per year, so I'll multiply the number of acres by 500 to get the total annual savings.Finally, I'll present both the number of acres and the total annual savings as the solution.
question：Sarah is a behavioral science student at an Ivy League university. For her research project, she needs to conduct surveys with students on campus to understand their study habits. She plans to survey a total of 120 students. She decides to survey students from three different departments: Psychology, Sociology, and Economics. She wants to survey twice as many Psychology students as Sociology students, and three times as many Economics students as Sociology students. How many students from each department does Sarah need to survey to reach her total of 120 students?
answer：First, I'll define variables to represent the number of students surveyed from each department. Let S be the number of Sociology students. According to the problem, the number of Psychology students is twice the number of Sociology students, so P = 2S. Similarly, the number of Economics students is three times the number of Sociology students, so E = 3S.Next, I'll set up an equation that sums up the total number of students surveyed: P + S + E = 120. Substituting the expressions for P and E in terms of S, the equation becomes 2S + S + 3S = 120.Combining like terms, this simplifies to 6S = 120. Solving for S, I divide both sides by 6, resulting in S = 20. Now, I'll calculate the number of students in each department. The number of Psychology students is P = 2S = 2 * 20 = 40. The number of Economics students is E = 3S = 3 * 20 = 60.Finally, I'll verify that the total number of students surveyed is 40 (Psychology) + 20 (Sociology) + 60 (Economics) = 120, which matches the required total.
question：As a project manager, you have a team of 5 developers. Each developer is assigned 3 tasks related to React.js every week. However, you need to provide additional guidance on best practices and project requirements for 2 of these tasks per developer. If you spend 30 minutes providing guidance on each task, how much total time in hours do you spend in a week guiding your team?
answer：First, I need to determine how many tasks require additional guidance. Each developer is assigned 3 tasks, and 2 of these need guidance. With 5 developers, the total number of tasks needing guidance is 5 multiplied by 2, which equals 10 tasks.Next, I calculate the total time spent on guidance. Each task requires 30 minutes of guidance. Therefore, for 10 tasks, the total time is 10 multiplied by 30 minutes, resulting in 300 minutes.Finally, I convert the total minutes into hours by dividing by 60. 300 minutes divided by 60 equals 5 hours.So, the total time spent guiding the team in a week is 5 hours.
question：Farmer Joe lives in a rural area and strongly believes that improving the roads will help local farmers transport their produce more efficiently, boosting the region's economy. Currently, it takes him 2 hours to transport 100 crates of vegetables to the market, traveling at an average speed of 30 miles per hour on the old, bumpy road. The local government plans to pave the road, which will allow Farmer Joe to travel at an average speed of 45 miles per hour. With this improvement, how much time will Farmer Joe save on a round trip to the market and back, assuming the distance to the market is 60 miles one way?
answer：First, I need to determine the total distance Farmer Joe travels for a round trip to the market and back. Since the one-way distance is 60 miles, the round trip distance is 120 miles.Next, I'll calculate the time it currently takes Farmer Joe to complete this round trip. He travels at an average speed of 30 miles per hour, so the time is 120 miles divided by 30 mph, which equals 4 hours.After the road is paved, Farmer Joe's average speed will increase to 45 miles per hour. I'll calculate the new time for the round trip by dividing the total distance of 120 miles by the new speed of 45 mph, resulting in approximately 2.67 hours.Finally, to find out how much time Farmer Joe will save, I'll subtract the new time from the original time: 4 hours minus 2.67 hours, which equals approximately 1.33 hours. This is equivalent to 1 hour and 20 minutes.
question：An Icelandic film enthusiast named Arnar loves to watch Rúnar Rúnarsson's movies. He decided to organize a film marathon where he would watch his five favorite Rúnar Rúnarsson films back-to-back. Each movie has a different length in minutes: the first movie is 95 minutes, the second is 110 minutes, the third is 88 minutes, the fourth is 105 minutes, and the fifth is 92 minutes. After each movie, Arnar takes a 10-minute break to avoid spoilers being discussed online.How many total minutes will Arnar spend on the film marathon, including the breaks between movies?
answer：First, I will add up the durations of all five movies to find the total movie time.Next, I will calculate the total break time by multiplying the number of breaks (which is one less than the number of movies) by the duration of each break.Finally, I will add the total movie time and the total break time to determine the overall time Arnar will spend on the film marathon.
question：A physical therapist has 5 clients that require 30 sessions in total. One of the clients needs 8 sessions. Another client needs 3 more than that. How many sessions would the remaining clients need?
answer：First, I recognize that there are 5 clients in total, and the total number of sessions required is 30.One client needs 8 sessions. Another client needs 3 more sessions than the first client, which means this client requires 11 sessions.Adding these together, the two clients account for 8 + 11 = 19 sessions.To find out how many sessions the remaining three clients need, I subtract the sessions already accounted for from the total: 30 - 19 = 11 sessions.Therefore, the remaining three clients need a total of 11 sessions.