A 26-mile circular marathon has four checkpoints inside it. The first is one mile from the start line, and the last checkpoint is one mile from the finish line. The checkpoints have equal spacing between them. How many miles apart are each of the consecutive checkpoints between the start-finish line?

The checkpoints are 1 mile from the start and finish, so they are spaced along 26 - 1 - 1 = 24 miles.

There are 4 equally spaced checkpoints, so the checkpoints are 24 / 4 =

<<24/4=6>>6 miles apart. #### 6 Buffy has a sailboat with a planing hull that she sails in the Gulf of Mexico. Under optimal wind conditions, the use of two sails brings the ship to the speed of 50 knots, whereas under the same conditions, the use of one sail brings her ship to the speed of 25 knots. A knot is a nautical term for speed equal to 1 nautical mile per hour, and one nautical mile equals 1.15 land miles. If she travels in her sailboat under optimal wind conditions for 4 hours with one sail and then for another 4 hours with two sails, what is the total distance, in land miles, that she will travel? Under optimal wind conditions, if her ship sails 4 hours with 1 sail, she will travel 4*25=<<4*25=100>>100 nautical miles. Under optimal wind conditions, if her ship sails 4 hours with 2 sails, she will travel 4*50=<<4*50=200>>200 nautical miles. In total, she will travel 100+200=<<100+200=300>>300 nautical miles. If 1 nautical mile is equivalent to 1.15 land miles, then Buffy will travel 300*1.15=<<300*1.15=345>>345 land miles. #### 345 You can lower the price by 20% if you buy more than fifteen units of iPhone cases. If you pay $500 to buy 18 units, what is the original price? If you buy 18 units, the percentage of the total price drops to 100% - 20% = 80% If 80% is equal to $500, then 100% is equals 100%/80% * $500 = $625 #### 625 Abraham is buying some toiletries and creates a budget of $60 for his shopping. He buys 4 shower gels for $4 each, a tube of toothpaste for $3, and a box of laundry detergent. If he has $30 remaining in his budget, how much money, in dollars, did Abraham spend on the box of laundry detergent? Shower gel costs Abraham 4 shower gels * $4 = $<<4*4=16>>16. So the shower gel and toothpaste combined have cost him $16 + $3 = $<<16+3=19>>19. He had money remaining in his budget so the total cost of his shopping must have been $60 – $30 = $<<60-30=30>>30. The box of laundry detergent therefore cost him $30 – $19 = $<<30-19=11>>11. #### 11 Annie goes to school. Today is her birthday, so Annie decided to buy some sweets for her colleagues. Every classmate got 2 candies. In the end, Annie got left with 12 candies. If there are 35 people in Annie's class in total, how much did Annie spend on candies, if one candy costs $0.1? There are 35 people in Annie's class, which means, she has 35 - 1 = <<35-1=34>>34 classmates. Every classmate got 2 candies, so in total Annie gave out 34 * 2 = <<34*2=68>>68 candies. In the beginning she had 68 + 12 = <<68+12=80>>80 candies. One candy costs $0.1, so Annie spend 80 * 0.1 = $<<80*0.1=8>>8 on candies. #### 8 Andrew eats 14 donuts on Monday, and half as many on Tuesday. On Wednesday Andrew eats 4 times as many as he did on Monday. How many donuts did Andrew eat total in the three days? Monday:14 Tuesday:14/2=7 Wednesday:4(7)=28 Total:14+7+28=<<14+7+28=49>>49 donuts #### 49 Solomon collected three times as many cans as Juwan. Levi collected half of what Juwan collected. Solomon collected 66 cans. How many cans did the boys collect in all? Solomon is 3*Juwan so Juwan is 1/3 of Solomon = 66/3 = 22 Levi collected half of 22 = <<22-11=11>>11 Combined the boys collected 66 + 22 + 11 = <<66+22+11=99>>99 cans in all. #### 99 Kimiko watches four YouTube videos. The first video is 2 minutes long, the second video is 4 minutes and 30 seconds, and the last two videos are equal in length. If she spends a total of 510 seconds watching YouTube, how many seconds long was each of the last two videos? First convert the length of the first video to seconds: 2 minutes * 60 seconds/minute = <<2*60=120>>120 seconds Then convert the length of the second video to seconds: 4 minutes * 60 seconds/minute + 30 seconds = 240 seconds + 30 seconds = <<4*60+30=270>>270 seconds Now subtract the length of the first two videos from the total time Kimiko spent watching to find the combined length of the last two videos: 510 seconds - 120 seconds - 270 seconds = <<510-120-270=120>>120 seconds Now divide the combined length by the number of videos to find each video's length: 120 seconds / 2 = <<120/2=60>>60 seconds #### 60 Justin wanted to watch a movie that came on at 8 pm that night. His parents agreed as long as he finished his homework and chores before the movie started. He wouldn't be home until 5 pm because of baseball practice. He knew dinner would take 45 minutes, and he figured his homework would take 30 minutes to finish. He needed to clean his room, which would take 30 minutes; then take out the trash, which would take about 5 minutes; and empty the dishwasher, which would take another 10 minutes. What was the latest time that Justin could start his chores and homework to be done by 8 pm to watch his movie? Justin would spend 45 minutes at dinner, 30 minutes doing homework, 30 minutes cleaning his room, 5 minutes on the trash and 10 on dishes for a total of 45+30+30+5+10 = <<45+30+30+5+10=120>>120 Justin knows that 60min is the same as 1 hour. He has 120 minutes of work so 120/60 = <<120/60=2>>2 hours His movie comes on at 8 pm and he has 2 hours of chores so 8-2 = <<8-2=6>>6 pm is the latest time he could start his chores #### 6 Kristine traveled to Paris in France to visit her friend. On the way, she has driven a train for 300 km and a bus for half that distance. After arriving in the city, she had to take a cab and drove three times fewer kilometers than she rode the bus. How many kilometers in total had Kristine traveled to reach her destination? Kristine traveled on the bus 300 km / 2 = <<300/2=150>>150 km. With the cab, she had to drive 150 km / 3 = <<150/3=50>>50 km. In total she had to cover 150 km + 50 km + 300 km = <<150+50+300=500>>500 km. #### 500