To get the number of people at Taylor's party, we'll assume there were n people at his party. The total number of people at Ryan's party is 4 * n, four times the number of attendees at Taylor's party. Combined, there were 4n + n = 240 people at both parties. This translates to 5n = 240. The total number of people at Taylor's party is n = 240 / 5. There were n = 48 people at Taylor's party. Since Ryan's party was 4 times as huge as Taylor's party, at Ryan's party, there were 48 * 4 = 192 people.
The answer: 192
Reverse engineering the question: Ryan's party was 4 times as huge as Taylor's birthday party. If both parties combined had 240 people, how many people were there at Ryan's party?
Reasoning and answer: The first 60 megabytes take 60 / 5 = 12 seconds. There are 90 - 60 = 30 remaining megabytes. The remaining 30 megabytes take 30 / 10 = 3 seconds. And 12 + 3 = 15 seconds.
The answer: 15
What was the question?
Question: The file, 90 megabytes in size, downloads at the rate of 5 megabytes per second for its first 60 megabytes, and then 10 megabytes per second thereafter. How long, in seconds, does it take to download entirely?
The carpenter initially has 8 x 5 = 40 blocks of wood. So he still lacks 80 - 40 = 40 blocks of wood. Therefore he still needs 40 / 5 = 8 logs of wood.
The answer: 8
Reverse engineering the question: A carpenter is building a house. He needs 80 woodblocks to build it. If he has 8 logs that can make five woodblocks each, how many logs does the carpenter still need?
Reasoning and answer: The cost of the ice cream is 10 $4 = $40. The cost of the frozen yoghurt is 4 $1 = $4. Caleb spent $40 $4 = $36 more on ice cream than on frozen yogurt.
The answer: 36
What was the question?
Question: Caleb bought 10 cartons of ice cream and 4 cartons of frozen yoghurt. Each carton of ice cream cost $4 and each carton of frozen yoghurt cost $1. How much more did Caleb spend on ice cream than on frozen yoghurt?
Jean already bought 15 cupcakes x 4 packs = 60 cupcakes. She needs 100 - 60 = 40 more cupcakes. Thus, she needs to buy 40 / 10 = 4 packs of 10 cupcakes.
The answer: 4
Reverse engineering the question: Cupcakes are sold in packages of 10 and 15. Jean bought 4 packs of 15 cupcakes. If she will give one cupcake each to 100 children in the orphanage, how many packs of 10 cupcakes should she need to buy?
60 mph is 60 * 1.5 = 90 feet per second. 40 mph is 40 * 1.5 = 60 feet per second. Thus, for every second, the cheetah advances on the gazelle by 90 - 60 = 30 feet per second. To close on a distance of 200 feet, it would take the cheetah 210 / 30 = 7 seconds to catch the gazelle.
The answer: 7
Reverse engineering the question:
A cheetah can run at a top speed of 60 mph. The gazelle can run for speeds of up to 40 miles per hour. If one mile per hour is about 1.5 feet per second, then how many seconds would it take for a cheetah traveling at top speed to catch up to a fleeing gazelle also running at top speed if the two animals were initially 210 feet apart and they both traveled in the same direction?