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## 2.4 Motion Problems & Consecutive Integers

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**Consecutive Integer Problems**• Integers • 2,3,4,5 • Even integers • 2,4,6,8 • Odd integers • 1,3,5,7 n, n+1, n+2, n+3 n, n+2, n+4, n+6 n, n+2, n+4, n+6**Example 1**• Parking spaces on the right are even and odd on the left. Two people on the left are parked next to each other. Their spaces have a sum of 80. What numbered spot are they each in? • Let x=1st odd person • Let x+2=2nd odd Person • x+x+2=80 • 2x+2=80 • 2x=78 • x=39 • So 1st person is #39, 2nd person is #41**Distance, Rate, Time (D=rt)**• Ex 2) Two people drive from Green Bay to Minneapolis, a total distance of 370 miles. The average driving speed of one driver is 16mph slower than that of the other. The faster driver drove for 2.5 hrs. and the slower driver a half hour longer. What was the average speed of each? 2.5r + 3(r-16) = 370 2.5r + 3r - 48 = 370 5.5r -48 = 370 5.5r = 418 R = 76 Slow is 60mph fast is 76mph Rate Time Distance Fast r 2.5 2.5r r-16 3 Slow 3(r-16) Totals 370**Motion Opposite Directions**• Ex 3) Two cars leave the same house at the same time. One traveling up North at 60mph and the other toward Chicago at 45mph. In how many hours will they be 420 miles apart? 60x+45x = 420 105x = 420 x = 4 4 hours Rate Time Distance Up North 60 x 60x 45 x Chicago 45x Totals 420**Motion Same Directions**• Ex 4) My wife gets up at 5am to go for her daily walk and travels at 3mph. I get up a half hour later and run at 5mph. How long till I catch her? 3(x+.5) = 5x 3x+1.5 = 5x 1.5 = 2x X=.75 Three fourths of an hour is 45 minutes! Rate Time Distance Mrs. LC 3 x+.5 3(x+.5) 5 x Mr. LC 5x Totals**HOMEWORK**Pg. 96:19-26,39-42