[Question]Jason is planning a parking garage that will have 12 floors. Every 3rd floor has a gate where drivers have to show ID, which takes two minutes. To get from one floor to the next, drivers have to drive 800 feet at 10 feet/second. How long, in seconds, does it take to get to the bottom of the garage from the top?
[Answer]First find the total number of gates someone has to pass through: 12 floors / 3 floors / gate = 4 gates. Then find the total time someone spends waiting at the gates: 4 gates * 2 minutes / gate = 8 minutes. Then convert that time to seconds: 8 minutes * 60 seconds / minute = 480 seconds. Then find the time to drive through one floor in seconds: 800 feet / 10 feet / second = 80 seconds. Then multiply the time per floor by the number of floors to find the total driving time: 80 seconds / floor * 12 floors = 960 seconds. Then add the total driving time to the total time waiting at the gates to find the total time to get to the bottom: 960 seconds + 480 seconds = 1440 seconds. The answer is 1440.
Q: Last month, a factory made 12000 dolls and their associated accessories. The accessories for each doll included 2 shoes, 3 bags, 1 set of cosmetics, and 5 hats. If each doll took 45 seconds to make and each accessory took 10 seconds to make, what was the total combined machine operation time, in seconds, required to manufacture all of the dolls and their accessories?
A: The number of shoes the factory made was 12000 dolls x 2 shoes / doll = 24000 shoes. The factory also made for each doll 12000 dolls x 3 bags / doll = 36000 bags. The set of cosmetics made for each doll was just one, so there are 12000 cosmetics sets. Finally, the number of hats for the dolls was 12000 dolls x 5 hats / doll = 60000 hats. In total, the number of accessories was 24000 + 36000 + 12000 + 60000 = 132000 accessories. The dolls took in total 12000 dolls x 45 seconds / doll = 540000 seconds to be made. All the accessories also took 132000 accessories x 10 seconds / accessory = 1320000 seconds. Combing both results, we have that the total time the machinery was working was 1320000 + 540000 = 1860000 seconds. The answer is 1860000.
Question: Andrew is having two of his friends over for a sleepover. For one friend, Brian, he asks his mother to buy 3 donuts. He asks for his other friend, Samuel, to get the same. A day before the sleepover Andrew ends up inviting two more friends and asks his mother to buy them the same amount of donuts. Just in case, Andrew's mother wants to buy one more donut for each of Andrew's friends. Andrew's mother is going to buy the same amount of donuts for Andrew as everybody else. How many donuts will Andrew's mother need to buy?
Answer: Andrew is having 4 friends over who will get 3 donuts each, 4 x 3 = 12 donuts total. Andrew's mother wants to get 1 extra donut for each of Andrew's friends, 3 donuts + 1 extra = 4 donuts for each of Andrew's friends. Andrew's mother is buying 12 + 4 extra donuts for Andrew's friends = 16 total donuts. Andrew's mother is also going to get 3 + 1 extra donut for Andrew = 4 donuts. Andrew's mother will need to buy 16 donuts for Andrew's friends + 4 donuts for Andrew = 20 total donuts. The answer is 20.
[Question]Stacy is a high school Calculus teacher. She assigns 45 problems for homework. There are twice as many multiple choice problems as free response, and 7 more free response than true/false. How many true/false questions are there?
[Answer]Let x represent the number of true / false questions. Free response:x + 7. Multiple choice: 2(x + 7) = 2x + 14. Total:x + x + 7 + 2x + 14 = 45. 4x + 21 = 45. 4x = 24. x = 6 true / false questions. The answer is 6.
Q: In five years, Grant will be 2/3 the age of the hospital that he is hired into. If Grant is currently 25 years old, how old is the hospital now?
A: If Grant is currently 25 years old, he will be 25 + 5 = 30 years old in five years. If 2 / 3 represents Grant's age in five years, then the fraction representing the number of years the hospital is older than Grant is 1 - 2 / 3 = 1 / 3. If 2 / 3 represents 30 years, 3 / 3, which is the fraction representing the age of the hospital, represents 3 / 3 * 30 * 3 / 2 = 45 years. Currently, the hospital is 45 - 5 = 40 years old. The answer is 40.
Question: Tony has to run several errands in a day. He needs to drive 10 miles to get groceries, 15 miles to get a haircut and 5 miles to go to a doctor's appointment. How many miles will Tony have driven when he is halfway through driving around for his errands?
Answer:
First, we need to find the total number of miles Tony will be driving by adding 10 + 15 + 5 = 30 miles in total. To determine the halfway point, we simply divide the total number of miles by 2, performing 30 / 2 = 15 miles driven when Tony is halfway done. The answer is 15.