Dana can run at a rate of speed four times faster than she can walk, but she can skip at a rate of speed that is half as fast as she can run. If she can skip at 3 miles per hour, how many miles can she travel in six hours if she spends one-third of the time running and two-thirds of the time walking?

How fast can Dana run? ** If Dana can skip at half the speed she can run, then she can run at 3*2=

<<3*2=6>>6 miles per hour. How fast can Dana walk? ** And since she can run at a speed that is 4 times faster than she can walk, this means she can walk at 6/4=1.5 miles per hour. How many hours does Dana walk? ** If two-thirds of the time is spent walking, then she walks for 6*(2/3)=<<6*(2/3)=4>>4 hours. How many hours does Dana run? ** If one-third of the time is spent running, then she runs for 6-4=<<6-4=2>>2 hours. How many miles does Dana run? ** Thus, she runs for 2 hours at 6 miles per hour, or 2*6=<<2*6=12>>12 miles. How many miles does Dana walk? ** She walks for 4 hours at 1.5 miles per hour, or 4*1.5=<<4*1.5=6>>6 miles. How many miles does Dana travel? ** Thus, altogether, she travels 12+6=<<12+6=18>>18 miles. #### 18 Brandon's iPhone is four times as old as Ben's iPhone. Ben's iPhone is two times older than Suzy's iPhone. If Suzy’s iPhone is 1 year old, how old is Brandon’s iPhone? How old is Ben's iPhone? ** Ben’s iPhone is 1*2 = <<1*2=2>>2 years old. How old is Brandon's iPhone? ** Brandon’s iPhone is 4*2 = <<4*2=8>>8 years old. #### 8 The great dragon, Perg, sat high atop mount Farbo, breathing fire upon anything within a distance of 1000 feet. Polly could throw the gold javelin, the only known weapon that could sleigh the dragon, for a distance of 400 feet, well within the reach of the dragon's flames. But when Polly held the sapphire gemstone, she could throw the javelin three times farther than when not holding the gemstone. If holding the gemstone, how far outside of the reach of the dragon's flames could Polly stand and still hit the dragon with the gold javelin? How far could Polly throw the gold javelin with the gemstone? ** With the gemstone, Polly could throw the javelin 3 times farther than 400 feet, for a distance of 3*400=<<3*400=1200>>1200 feet. How far beyond the reach of the dragon's flames could Polly stand and still hit the dragon with the gold javelin? ** 1200 feet is beyond the 1000-foot reach of the dragon's flames by a distance of 1200-1000=<<1200-1000=200>>200 feet. #### 200 Grandma Jones baked 5 apple pies for the fireman's luncheon. She cut each pie into 8 pieces and set the five pies out on the buffet table for the guests to serve themselves. At the end of the evening, after the guests had taken and eaten their pieces of pie, there were 14 pieces of pie remaining. How many pieces were taken by the guests? How many pieces were there at the start of the evening? ** To start the evening, there were 5 pies, each with 8 pieces, which is 5*8=<<5*8=40>>40 pieces of pie. How many pieces were taken by the guests? ** If only 14 remained, then 40-14=<<40-14=26>>26 pieces of pie had been taken by guests. #### 26 According to its nutritional info, a bag of chips has 250 calories per serving. If a 300g bag has 5 servings, how many grams can you eat if your daily calorie target is 2000 and you have already consumed 1800 calories? How many calories do I have left to eat? ** If the total calorie target is 2000 and I have consumed 1800 calories then I have 2000-1800 = <<2000-1800=200>>200 calories left to eat How many servings can I eat? ** If each serving of chips has 250 calories and I only have 200 calories left to eat, then I can only eat 200/250 of a serving = 4/5 of a serving How many grams are in each serving? ** We also know that a 300g bag of chips has 5 servings, hence each serving has 300g/5 = <<300/5=60>>60 grams How many grams can I eat? ** If I can only eat 4/5 of a serving, then I can eat only 60g * 4/5 = 240g/5 = 48 grams #### 48 Charlie wants to sell beeswax candles. For every pound of beeswax, he can make 10 tapered candles. One pound of beeswax and the wicks cost $10.00 in supplies. If he sells each candle for $2.00 each, what is his net profit if he makes and sells 20 candles? How many pounds of beeswax does Charlie need? ** 1 pound of beeswax and the wick make 10 candles and he wants to make 20 candles so he needs 20/10 = <<20/10=2>>2 pounds of beeswax How much will the supplies cost? ** 1 pound of beeswax costs $10.00 and he needs 2 pounds so his supplies will cost 10*2 = $<<10*2=20.00>>20.00 How much will each candle cost? ** He wants to sell each candle for $2.00 each and he's selling 20 candles so that's 2*20 = $<<2*20=40.00>>40.00 What is Charlie's net profit? ** If he makes $40.00 selling candles and his supplies cost $20.00 then his net profit is 40-20 = $<<40-20=20.00>>20.00 #### 20 Meredith is a freelance blogger who writes about health topics and submits to clients each day as her permanent job. A blog article takes an average of 4 hours to research and write about. Last week, she wrote 5 articles on Monday and 2/5 times more articles on Tuesday than on Monday. On Wednesday, she wrote twice the number of articles she wrote on Tuesday. Calculate the total number of hours she spent writing articles in the three days. How many more articles did Meredith write on Tuesday than on Monday? ** If she wrote five articles on Monday, then on Tuesday she wrote 2/5* 5 = 2 more articles. How many articles did Meredith write on Tuesday? ** The total number of articles she wrote on Tuesday is 5+2 = <<5+2=7>>7 How many articles did Meredith write on Wednesday? ** On Wednesday, the number of articles was twice the number she wrote on Tuesday, so it was 2*7 = <<2*7=14>>14 articles. How many articles did Meredith write in the three days? ** Over the three days, she wrote 5+7 +14 = <<5+7+14=26>>26 articles. How many hours did Meredith spend writing articles in the three days? ** If each article takes her 4 hours to research and write about, she spent 4*26 = <<4*26=104>>104 hours on all the articles. #### 104 Candice put 80 post-it notes in her purse before she headed out to her job at the coffee shop. On her way, she stopped off at the store and purchased a package of Post-it notes; At work, she placed a single Post-it note on each of 220 different cups of coffee. If she had 23 post-it notes remaining overall, how many Post-it notes were in the package that she purchased? Define a variable ** Let's let x be the number of post-it notes in the package that Candice purchased. How many post-it notes did Candice have when she left the store? ** Then, the total number of post-it notes she had when she left the store was 80+x. Write an equation ** And if she used 220 Post-it notes at work and had 23 left, then 80+x=220+23 How many Post-it notes were in the package that Candie purchased? ** Subtracting 80 from each side of the equation, we see that x=220+23-80=<<220+23-80=163>>163 Post-it notes. #### 163 John buys twice as many red ties as blue ties. The red ties cost 50% more than blue ties. He spent $200 on blue ties that cost $40 each. How much did he spend on ties? How many blue ties did John buy? ** He bought 200 / 40 = <<200/40=5>>5 blue ties How many red ties did John buy? ** So he bought 5 * 2 = <<5*2=10>>10 red ties How much do red ties cost? ** Each red tie cost $40 * .5 = $<<40*.5=20>>20 more than blue ties How much do red ties cost? ** So they each cost $40 + $20 = $<<40+20=60>>60 How much did John spend on red ties? ** So he spent $60 * 10 = $<<60*10=600>>600 on red ties How much did John spend on ties? ** So he spent $200 + $600 = $<<200+600=800>>800 on ties #### 800 Tracy used a piece of wire 4 feet long to support tomato plants in the garden. The wire was cut into pieces 6 inches long. How many pieces did she obtain? How many inches was the wire? ** If Tracy used a piece of wire 4 feet long, since 1 foot is equal to 12 inches, the total length of the wire in inches was 12*4=<<12*4=48>>48 inches. How many pieces did Tracy obtain? ** Since the wire was cut into pieces 6 inches long, Tracy obtained 48/6=<<48/6=8>>8 pieces #### 8