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Lesson 92 Uniform Motion Problems About Equal Distances

LESSON PRESENTATION. Example 92.1. Example 92.2. Example 92.3. Lesson 92 Uniform Motion Problems About Equal Distances. Uniform Motion. Uniform motion refers to objects traveling along a straight line with a constant speed (velocity).

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Lesson 92 Uniform Motion Problems About Equal Distances

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  1. LESSON PRESENTATION Example 92.1 Example 92.2 Example 92.3 Lesson 92 Uniform Motion Problems About Equal Distances

  2. Uniform Motion Uniform motion refers to objects traveling along a straight line with a constant speed (velocity). The distance an object travels is equal to the speed the object is traveling (rate) mutliplied by the time the object is in motion. Distance = Rate X Time The distance(D) an object travels at (R) speed in (T) time is modeled by the following formula: D = RT

  3. Uniform Motion D1 D1 (a) (b) D2 D2 The statements of the distances discussed in these problems can be represented graphically by drawing diagrams in which arrows represent distances. In these problems we will usually be working with problems that describe two distances. In this lesson we will investigate problems involving equal distances that can be represented using one of the following diagrams. D1 = D2

  4. Uniform Motion D1 D1 (a) (b) D2 D2 The statements of the distances discussed in these problems can be represented graphically by drawing diagrams in which arrows represent distances. In these problems we will usually be working with problems that describe two distances. In this lesson we will investigate problems involving equal distances that can be represented using one of the following diagrams. D1 = D2

  5. Example 92.1 DE DF On Tuesday the express train made the trip in 12 hours. On Wednesday the freight train made the same trip in 16 hours. Find the rate of each train if the rate of the freight train was 15 kilometers per hour less than the rate of the express train. First: Draw the diagram. DE = DF RE TE = RF TF TE = 12 TF = 16 RE = RF +15 (RF +15)(12) = RF (16) RE = 45+15 12RF + 180 = 16RF RE = 60 kmph - 4RF= -180 The rate of the express train was 60 kmph and the rate of the freight train was 45 kmph. RF= 45kmph

  6. Example 92.2 DH DR The members of the girls club hiked to Lake Tenkiller at 2 miles per hour. Mr. Ali gave them a ride back home at 12 miles per hour. Find their hiking time if it was 5 hours longer than their riding time. How far was it to Lake Tenkiller? First: Draw the diagram. DH = DR RH TH = RR TR RH = 2 RR = 12 TH = TR +5 (2)TH= 12(TH- 5 ) TH- 5 = TR DH = RH TH 2TH= 12TH -60 DH = (2)(6) - 10TH= -60 DH = 12 miles TH= 6 hrs Their hiking time was 6 hours and the distance to Lake Tenkiller was 12 miles.

  7. Example 92.3 DD DW Durant drove to the oasis in 2 hours and Madill walked to the oasis in 10 hours. How far is it to the oasis if Durant drove 16 miles per hour faster than Madill walked? First: Draw the diagram. DD = DW RD TD = RW TW RD = RW + 16 TD = 2 (RW + 16)(2) = RW(10) TW = 10 DW = RW TW 2RW + 32 = 10RW DW = (4)(10) 32 = 8RW DW = 40 miles 4 = RW It is 40 miles to the oasis.

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