Bob runs 6 miles per hour. His friend Jim runs at 9 miles per hour. If Bob has a 1 mile head-start, how many minutes will it take before Jim catches him?

How many miles does Bob run in a minute? ** Bob runs .1 miles per minute because 6 / 60 =

<<6/60=.1>>.1 How many miles does Jim run in a minute? ** Jim run at .15 miles per minute 9 / 60 = <<9/60=.15>>.15 How many minutes does it take Jim to catch Bob? ** We know that .1(Number of Minutes) + 1 = .15(Number of Minutes) How many minutes does it take Jim to catch Bob? ** Therefore 1 = .05(Number of minutes) How many minutes does it take Jim to catch Bob? ** Therefore (Number of minutes) = 20 because 1 / .05 = <<1/.05=20>>20 #### 20 A flagpole is 12 feet tall. It breaks, folding over in half, such that what was the tip of the flagpole is now dangling two feet above the ground. How far from the base, in feet, did the flagpole break? How many feet from the top did the break occur? ** The break occurred (12-2)/2=5 feet from the top. How far from the base, in feet, did the flagpole break? ** Then it was 12-5=<<12-5=7>>7 feet from the base. #### 7 Paige bought some new stickers and wanted to share them with 3 of her friends. She decided to share a sheet of 100 space stickers and a sheet of 50 cat stickers equally among her 3 friends. How many stickers will she have left? How many space stickers will Paige give to each friend? ** Paige has 100 space stickers that she is dividing among 3 friends, so 100 stickers / 3 friends = 33 stickers for each friend, with 1 remaining. How many cat stickers will Paige give to each friend? ** She also has 50 cat stickers that she is diving among 3 friends, so 50 stickers / 3 friends = 16 stickers for each friend, with 2 remaining. How many stickers will Paige have left? ** So Paige will have 1 remaining space sticker + 2 remaining cat stickers = <<1+2=3>>3 stickers left. #### 3 Matthew, the baker, arrives at work early every morning to make his famous caramel-apple coffee cakes for the day. It usually takes Matthew 1 hour to assemble ingredients, 1.5 hours to bake the cakes, and another 1 hour to decorate each cake with cinnamon sprinkles. One day, Matthew's oven failed to reach the correct temperature and it took twice as long for the cakes to bake as they usually take. On that day, how long did it take, in hours, for Matthew to make his famous caramel-apple coffee cakes? How long did it take to bake the cakes? ** Twice 1.5 hours is 2*1.5=<<2*1.5=3>>3 hours. How long did it take, in hours, for Matthew to make his famous caramel-apple coffee cakes? ** Thus, on that day, it took Matthew 1+3+1=<<1+3+1=5>>5 hours to make the cakes. #### 5 In 2021, Wayne is 37 years old. His brother Peter is 3 years older than him and their sister Julia is 2 years older than Peter. What year was Julia born in? How old is Peter? ** Peter is 3 years older than Wayne who is 37 so Peter is 37+3 = <<37+3=40>>40 years old How old is Julia? ** Julia is 2 years older than Peter who is 40 so Julia is 2+40 = <<2+40=42>>42 years old What year was Julia born in? ** It's 2021 and Julia is 42 years old so she was born in 2021-42 = <<2021-42=1979>>1979 #### 1979 John decided to buy 10 pins for himself. They are normally $20 each but they were on sale for 15% off. How much did he spend on pins? How much did the sell reduce the price of each pin? ** The sell reduced the price of each pin by 20*.15=$<<20*.15=3>>3 How much did John pay for each pin? ** So he paid 20-3=$<<20-3=17>>17 per pin How much did John spend on pins? ** So the total cost was 17*10=$<<17*10=170>>170 #### 170 Apple and peach trees are planted in the orchard of the Grange Poser farm. The orchard has 30 apple trees that each give 150 kg of apples and 45 peach trees that each produce an average of 65 kg of fruit. What is the total mass of fruit harvested in this orchard? How many apples do the apple trees produce? ** Let’s first calculate what the apple trees produce: 30 trees * 150 kg/tree = <<30*150=4500>>4500 kg How many peaches do the peach trees produce? ** Then let's calculate what the peaches produce: 45 trees * 65 kg/tree = <<45*65=2925>>2925 kg What is the total mass of fruit harvested in this orchard? ** We add these two masses: 4500 kg + 2925 kg = <<4500+2925=7425>>7425 kg #### 7425 Winston has 14 quarters. He then spends half a dollar on candy. How many cents does he have left? How many quarters does Winston have? ** Winston has 350 cents because 14 x 25 = <<14*25=350>>350 How much does Winston spend? ** He spends 50 cents because $1 / 2 = 50 cents How many cents does Winston have left? ** He has 300 cents left at the end. #### 300 To get the printer to work, Jerry needs to add a black-and-white cartridge and three color cartridges. If each color cartridge costs $32 and each black-and-white cartridge costs $27, how much does he pay total? How much do the color cartridges cost? ** First find the total cost of the color cartridges: $32/cartridge * 3 cartridges = $<<32*3=96>>96 How much do the color and black-and-white cartridges cost together? ** Then add the cost of the black-and-white cartridge to find the total cost: $96 + $27 = $<<96+27=123>>123 #### 123 A choir was singing a song that involved 30 singers. In the first verse, only half of them sang. In the second verse, a third of the remaining singers joined in. How many people joined in the final third verse that the whole choir sang together? How many singers sang in the first verse? ** In the first verse, 30 / 2 = <<30/2=15>>15 singers sang. How many singers joined in the second verse? ** In the second verse, 15 / 3 = <<15/3=5>>5 singers joined in. How many singers joined in the final third verse that the whole choir sang together? ** In the final verse, 30 - 15 - 5 = <<30-15-5=10>>10 singers joined for the whole choir to sing together. #### 10