Q: Conner has a dune buggy that he rides in the desert. On flat sand, it can ride at a speed of 60 miles per hour. When traveling on downhill slopes, it can race at 12 miles per hour faster than it can when it is on flat sand. And when riding on an uphill inclined slow, it travels at a speed 18 miles per hour slower than when it is riding on flat sand. If Conner rides his dune buggy one-third of the time on flat sand, one-third of the time on uphill slopes, and one-third of the time on downhill slopes, what is his average speed in miles per hour?
A: 12 mph faster than 60mph is 60 + 12 = 72 mph. 18 mph slower than 60 mph is 60 - 18 = 42 mph. If he spends 1 / 3 of the time at each of these three speeds, then he averages (60 + 72 + 42) / 3 = 58 mph. The answer is 58.
Question: In a race, there are eight runners. The first five runners finish the race in 8 hours, while the rest of the runners finish the race 2 hours later. Calculate the total time the eight runners took to finish the race.
Answer: The first five runners took a combined total of 5 * 8 = 40 hours to finish the race. The number of runners who finished the race 2 hours later after the first five is 8 - 5 = 3. The 3 runners who finished the race 2 hours later took a total of 8 + 2 = 10 hours to run the race. Together, the three runners who finished the race in 10 hours took a total of 10 * 3 = 30 hours. All eight runners took 30 + 40 = 70 hours altogether to finish the race. The answer is 70.
[Question]You can buy 4 apples or 1 watermelon for the same price. You bought 36 fruits evenly split between oranges, apples and watermelons, and the price of 1 orange is $0.50. How much does 1 apple cost if your total bill was $66?
[Answer]If 36 fruits were evenly split between 3 types of fruits, then I bought 36 / 3 = 12 units of each fruit. If 1 orange costs $0.50 then 12 oranges will cost $0.50 * 12 = $6. If my total bill was $66 and I spent $6 on oranges then I spent $66 - $6 = $60 on the other 2 fruit types. Assuming the price of watermelon is W, and knowing that you can buy 4 apples for the same price and that the price of one apple is A, then 1W = 4A. If we know we bought 12 watermelons and 12 apples for $60, then we know that $60 = 12W + 12A. Knowing that 1W = 4A, then we can convert the above to $60 = 12(4A) + 12A. $60 = 48A + 12A. $60 = 60A. Then we know the price of one apple (A) is $60 / 60 = $1. The answer is 1.
Q: Justin bought some jerseys. He bought four long-sleeved ones that cost $15 each, and some striped ones that cost $10 each. How many striped jerseys did Justin buy if he spent a total of $80?
A: Four long - sleeved jerseys cost $15 x 4 = $60. So the striped jerseys amount to $80 - $60 = $20. Hence, Justin bought $20 / $10 = 2 striped jerseys. The answer is 2.
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?
Answer: 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 is 7.
Q: Gretchen's local ice cream shop offers 100 different flavors. She was able to try a 1/4 of the flavors 2 years ago and double that amount last year. How many more flavors will she need to try this year to have tried all 100 flavors?
A:
The shop offers 100 flavors and she tried 1 / 4 of the flavors so she had 100 * .25 = 25 flavors 2 years ago. Last year she ate double the amount from the previous year so she had 25 * 2 = 50 flavors. 2 years ago she ate 25 flavors and last year she had 50 flavors so she has had 25 + 50 = 75 flavors. The shop offers 100 flavors and she has had 75 flavors so she still needs to try 100 - 75 = 25 flavors. The answer is 25.