CHAPTER+5+WORD+PROBLEMS

 **RATE x TIME = WORK word problems:** . Crane A can unload the container ship in 10 hours, and crane B can unload the ship in 14 hours. Crane A started to unload the ship at noon and was joined by crane B at 2 p.m. At what time was the unloading of the ship completed? || ||= t-2 ||= (t-2)/14 || //t = the number of hours crane A worked t-2 = the number of hours crane B worked  **. The part done by Crane A plus the part done by Crane B is one whole job. t/10 +(t-2)/14 = 1 LCM = 70 7t +5t - 10 = 70 12t = 80 t = 80/12 = 20/3 = 6 2/3 Answer: 6:40 p.m.** **.**  **MEMBERSHIP word problems: .** The Hiking Club collected the same amount from each member participating in a hiking trip in the mountains. When six members could not attend, each of the remaining members were charged 2 dollars more to cover the total cost of 360 dollars. How many members went on the hike?     //x = the number of people originally going x-6 = the number of people actually going 360/x + 2 = 360/(x-6) 360(x-6) + 2x(x-6) = 360x 360x -2160+2x^2**-12x = 360x **-12x -2160 = 0 (x-36)(x+30)= o {36, -30} x = 36 x-6 = 36-6 = 30 Answer: 30 members** . || Number || Value || Total || || 5 L || .25 || 1.25 || || x || .75 || .75x || || 5 L || <span style="DISPLAY: block; COLOR: #afe4a0; FONT-FAMILY: Georgia, serif; BACKGROUND-COLOR: #000000; TEXT-ALIGN: center">.55 || <span style="DISPLAY: block; COLOR: #afe4a0; FONT-FAMILY: Georgia, serif; BACKGROUND-COLOR: #000000; TEXT-ALIGN: center">2.75 || <span style="DISPLAY: block; COLOR: #afe4a0; FONT-FAMILY: Georgia, serif; BACKGROUND-COLOR: #000000; TEXT-ALIGN: center">//x = the number of liters that must be drawn and replaced// <span style="DISPLAY: block; COLOR: #afe4a0; FONT-FAMILY: Georgia, serif; BACKGROUND-COLOR: #000000; TEXT-ALIGN: center">**1.25 - .25x + .75x = 2.75 .5x = 1.5 x = 3 Answer: 3 Liters
 * =  ||= Rate ||= Time ||= Word ||
 * = Crane A ||= 1/10 ||= t ||= t/10
 * = Crane B ||= 1/14
 * Since crane A can do the job in 10 hours, it can do 1/10 of the job in one hour and crane B can do 1/14 of the job in one hour.//
 * = <span style="DISPLAY: block; COLOR: #f68888; FONT-FAMILY: Georgia, serif; BACKGROUND-COLOR: #000000; TEXT-ALIGN: center">        ||= ** <span style="DISPLAY: block; COLOR: #f68888; FONT-FAMILY: Georgia, serif; BACKGROUND-COLOR: #000000; TEXT-ALIGN: center"> Number   ** ||= ** <span style="DISPLAY: block; COLOR: #f68888; FONT-FAMILY: Georgia, serif; BACKGROUND-COLOR: #000000; TEXT-ALIGN: center"> Value   ** ||= ** <span style="DISPLAY: block; COLOR: #f68888; FONT-FAMILY: Georgia, serif; BACKGROUND-COLOR: #000000; TEXT-ALIGN: center"> Total   ** ||
 * = ** <span style="DISPLAY: block; COLOR: #f68888; FONT-FAMILY: Georgia, serif; BACKGROUND-COLOR: #000000; TEXT-ALIGN: center"> Before  ** ||= ** <span style="DISPLAY: block; COLOR: #f68888; FONT-FAMILY: Georgia, serif; BACKGROUND-COLOR: #000000; TEXT-ALIGN: center"> x   ** ||= ** <span style="DISPLAY: block; COLOR: #f68888; FONT-FAMILY: Georgia, serif; BACKGROUND-COLOR: #000000; TEXT-ALIGN: center"> 360/x   ** ||= ** <span style="DISPLAY: block; COLOR: #f68888; FONT-FAMILY: Georgia, serif; BACKGROUND-COLOR: #000000; TEXT-ALIGN: center"> 360   ** ||
 * = ** <span style="DISPLAY: block; COLOR: #f68888; FONT-FAMILY: Georgia, serif; BACKGROUND-COLOR: #000000; TEXT-ALIGN: center"> After  ** ||= ** <span style="DISPLAY: block; COLOR: #f68888; FONT-FAMILY: Georgia, serif; BACKGROUND-COLOR: #000000; TEXT-ALIGN: center"> x-6   ** ||= ** <span style="DISPLAY: block; COLOR: #f68888; FONT-FAMILY: Georgia, serif; BACKGROUND-COLOR: #000000; TEXT-ALIGN: center"> 360/(x-6)   ** ||= ** <span style="DISPLAY: block; COLOR: #f68888; FONT-FAMILY: Georgia, serif; BACKGROUND-COLOR: #000000; TEXT-ALIGN: center"> 360   ** ||
 * nV=T therefore V = T/n//
 * The original cost plus 2 dollars is the actual cost
 * <span style="DISPLAY: block; COLOR: #afe4a0; FONT-FAMILY: Georgia, serif; BACKGROUND-COLOR: #000000; TEXT-ALIGN: center">SOLUTION word problems: **  <span style="DISPLAY: block; COLOR: #afe4a0; FONT-FAMILY: Georgia, serif; BACKGROUND-COLOR: #000000; TEXT-ALIGN: center">.
 * A car radiator is filled with 5 liters of a 25% antifreeze solution. How many liters must be drawn off and replaced by a 75% solution antifreeze solution to leave the radiator filled with a 55% antifreeze solution?**
 * <span style="DISPLAY: block; COLOR: #afe4a0; FONT-FAMILY: Georgia, serif; BACKGROUND-COLOR: #000000; TEXT-ALIGN: center">Solutions
 * <span style="DISPLAY: block; COLOR: #afe4a0; FONT-FAMILY: Georgia, serif; BACKGROUND-COLOR: #000000; TEXT-ALIGN: center">25% solution
 * <span style="DISPLAY: block; COLOR: #afe4a0; FONT-FAMILY: Georgia, serif; BACKGROUND-COLOR: #000000; TEXT-ALIGN: center">75% solution
 * <span style="DISPLAY: block; COLOR: #afe4a0; FONT-FAMILY: Georgia, serif; BACKGROUND-COLOR: #000000; TEXT-ALIGN: center">Mixture ( 55% solution)
 * The 25% solution minus x amount of the 25% solution plus x amount of the 75% solution is the 55% solution**.

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