James is trying to decide which trail is faster to hike. One trail is 20 miles and mostly downhill, so James can cover it at 5 miles per hour. The other trail is 12 miles, but it's mostly uphill, so James will only be able to cover 3 miles per hour and will have to take an hour break halfway through. How many hours faster is the fastest hike?

First find how long the first trail takes to hike: 20 miles / 5 miles/hour =

<<20/5=4>>4 hours Then find how long James spends hiking the second trail: 12 miles / 3 miles/hour = <<12/3=4>>4 hours Then add the 1 hour break James has to take on the second trail: 4 hours + 1 hour = <<4+1=5>>5 hours Then subtract the time for the first trail from the time for the second trail to find the difference: 5 hours - 4 hours = <<5-4=1>>1 hour #### 1 A train takes 2 hours longer to go an equal distance of a car. If the car and the train leave station A at the same time, and the car reaches station B 4.5 hours later, calculate the combined time the car and the train take to reach station B. Since the train takes 2 hours longer to go an equal distance as the car, to reach station B, the train took 4.5+2 = 6.5 hours. Together, the train and the car take a total of 6.5+4.5 = <<6.5+4.5=11>>11 hours to travel from station A to station B. #### 11 There are 30 players on a football team. The coach has 8 liters of water. She pours 200 milliliters of water for every player so they can get hydrated. Unfortunately, there was a water spill and 250ml of water was spilled. How much water was left over? The coach has 8 liters * 1000 ml/liter = <<8000=8000>>8,000 ml of water. She pours 200 ml/player x 30 players = <<200*30=6000>>6,000 ml of water in total for all the athletes. The water spill means 6,000 ml + 250 ml = <<6000+250=6250>>6,250 ml of water was used. There was 8,000 ml - 6,250 ml = <<8000-6250=1750>>1,750 ml of water left. #### 1750 Ben wants to pick 56 sugar snap peas. At his current rate of picking, all will be picked in seven minutes. How long, in minutes, would it take Ben to pick 72 sugar snap peas? In 1 minute, Ben picks 56/7=<<56/7=8>>8 sugar snap peas. Ben would take 72/8=<<72/8=9>>9 minutes to pick 72 sugar snap peas. #### 9 Peter has to walk 2.5 miles to get to the grocery store. If it takes him 20 minutes to walk one mile and he has walked 1 mile already, how many more minutes does he have to walk to reach it? Peter has to walk a remaining 2.5 total miles - 1 mile completed = <<2.5-1=1.5>>1.5 miles remaining It will take him another 20 minutes * 1.5 miles remaining = <<20*1.5=30>>30 minutes to get to the grocery store #### 30 Adrian has the choice between two boxes of contacts. One has 50 contacts for $25, and the other has 99 contacts for $33. He chooses the box that costs less per individual contact. How many contacts will it take to equal $1 worth in whatever box he decides to buy? First, we need to determine the price per contact in each of the two choices. We begin by performing 50/25= <<50/25=2>>2 contacts per every dollar spent on choice A. Next, we determine the price per contact of the alternate choice. We do this by performing 99/33= <<99/33=3>>3 contacts for every dollar spent on choice B. Since 3>2, Adrian purchases choice B. The answer is therefore 3. #### 3 The size of a bathroom is 96 sq ft. If the width of the bathroom is 8 feet and the owner wants to extend it by 2 feet on each side, what is the new area of the bathroom? The original length of the bathroom is 96 sq ft/8 ft = <<96/8=12>>12 ft The new length of the bathroom is 12ft + 2 ft = <<12+2=14>>14 ft The new width of the bathroom is 8 ft + 2 ft = <<8+2=10>>10 ft The new area of the bathroom is 14ft x 10 ft = <<14*10=140>>140 sq ft #### 140 Mary tried to improve her health by changing her diet, but her weight bounced like a yo-yo. At first, she dropped a dozen pounds. Then, she added back twice the weight that she initially lost. Then, she dropped three times more weight than she initially had lost. But finally, she gained back half of a dozen pounds. If she weighed 99 pounds at the start of her change in diet, what was her final weight, in pounds? Since Mary first weighed 99 pounds, after she dropped a dozen pounds she weighed 99-12=<<99-12=87>>87 pounds. Twice the weight she initially lost is 12*2=<<12*2=24>>24 pounds. So, when she added back twice the weight that she initially lost, her weight jumped to 87+24=<<87+24=111>>111 pounds. Three times more than she initially had lost is 12*3=<<12*3=36>>36 pounds. Therefore, when Mary lost 3 times more than she initially lost, her weight dropped to 111-36=<<111-36=75>>75 pounds. Finally, when Mary gained back half of a dozen pounds, her final weight was 75+6=<<75+6=81>>81 pounds. #### 81 There are 480 zombies in the shopping mall. If the number of zombies doubled every day, how many days ago were there less than 50 zombies in the mall? First find how many zombies there were one day ago: 480 zombies / 2 = <<480/2=240>>240 zombies Then find how many zombies there were two days ago: 240 zombies / 2 = <<240/2=120>>120 zombies Then find the number of zombies there were three days ago: 120 zombies / 2 = <<120/2=60>>60 zombies Then find the number of zombies there were four days ago: 60 zombies / 2 = <<60/2=30>>30 zombies, which is less than 50, so there were less than 50 zombies 4 days ago. #### 4 In 2004, there were some kids at a cookout. In 2005, half the number of kids came to the cookout as compared to 2004. In 2006, 2/3 as many kids came to the cookout as in 2005. If there were 20 kids at the cookout in 2006, how many kids came to the cookout in 2004? In 2005, 20/2*3=<<20/2*3=30>>30 kids came to the cookout. In 2004, 30*2=<<30*2=60>>60 kids came to the cookout. #### 60