Rick likes to separate his collection of books into various groups by genre. He has 400 books in total and proceeds to divide them into two separate equally-sized categories repeatedly until he has each book in a category with 24 other books. How many times must he break these groups into smaller groups to accomplish this?
Let's think: Rick starts with 400 books and divides them into two categories of equal size, meaning there are two categories of 400 / 2 = 200 books. Rick repeats this process again, dividing the 200 book categories into equal halves, leaving him with 200 / 2 = 100 books in each. Rick repeats this process again, dividing the 100 book categories into equal halves, leaving him with 100 / 2 = 50 books in each. Rick repeats this process again, dividing the 50 book categories into equal halves, leaving him with 50 / 2 = 25 books in each. Since Rick is looking for categories with 25 books in each, he accomplishes this by the 4th step.. The answer is: 4.

Camila has only gone hiking 7 times in her life. Amanda has gone on 8 times as many hikes as Camila, and Steven has gone on 15 more hikes than Amanda. If Camila wants to say that she has hiked as many times as Steven and plans to go on 4 hikes a week, how many weeks would it take Camila to achieve her goal?
Let's think: Amanda has gone on 7 hikes x 8 = 56 hikes. Steven has gone on 56 hikes + 15 hikes = 71 hikes. Camila needs to go on another 71 hikes - 7 hikes = 64 hikes. Camila will achieve her goal in 64 hikes / 4 hikes / week = 16 weeks.. The answer is: 16.

A single train car can carry 60 passengers. A 747 airplane can carry 366 passengers. How many more passengers can a train with 16 cars carry than 2 airplanes?
Let's think: A train with sixteen cars can carry 16 x 60 = 960 passengers. 2 airplanes can carry 2 x 366 = 732 passengers. The train can carry 960 - 732 = 228 passengers more than 2 airplanes.. The answer is: 228.

Mary and Ann are going sledding. Mary slides down a hill that's 630 feet long at a speed of 90 feet/minute. Ann slides down a hill that's 800 feet long at a rate of 40 feet/minute. How much longer does Ann's trip take than Mary?
Let's think:
First find the total time Mary's trip takes: 630 feet / 90 feet / minute = 7 minutes. Then find the total time Ann's trip takes: 800 feet / 40 feet / minute = 20 minutes. Then subtract Mary's time from Ann's time to find the difference: 20 minutes - 7 minutes = 13 minutes.. The answer is: 13.