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Prepared by: David Crockett Math Department Lesson 94 Uniform Motion Problems of the Form D 1 +D 2 = N Example 94.3Example 94.2Example 94.1 LESSON PRESENTATION

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Prepared by: David Crockett Math Department Uniform Motion The uniform motion problems we worked earlier (Lesson 92) were about equal distances. The diagrams representing that motion are below. (a) D1D1 D2D2 (b) D1D1 D2D2 D 1 = D 2 and R 1 T 1 = R 2 T 2

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Prepared by: David Crockett Math Department Uniform Motion The uniform motion problems we will learn in this lesson will involve objects in motion in such a way that the sum of their distances are equal to a certain value. D1D1 D 1 + D 2 = N and R 1 T 1 + R 2 T 2 = N D2D2 D1D1 D2D2

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Prepared by: David Crockett Math Department Example 94.1 A southbound bus left Fort Walton Beach at 9 a.m. Two hours later a northbound bus left the same station. If the buses traveled at the same rate and were 352 kilometers apart at 2 p.m., find the rate of the buses. First: Draw the diagram. D S + D N = 352 R S T S + R N T N = 352T S = 5T N = 3R S = R N R S (5) + R S (3) = 352 8R S = 352 R S = kmph The buses were traveling at a rate of 44 kmph. DSDS DNDN

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Prepared by: David Crockett Math Department Example 94.2 A train starts from Toledo at 11 a.m. and heads for Mackinaw, 332 kilometers away. At the same time, a train leaves Mackinaw and heads to Toledo at 65 kilometers per hour. If the trains meet at 1 p.m., what was the rate of the first train. First: Draw the diagram. D 1 + D 2 = 332 R 1 T 1 + R 2 T 2 = 332T 1 = T 2 = 2R 2 = 65 R 1 (2) + (65) (2) = 332 The rate of the first train was 101 kmph. D1D1 D2D2 R 1 = ??? 2R = 332 2R 1 = 202 R 1 = 101 kmph

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Prepared by: David Crockett Math Department Example 94.3 The ships were 400 miles apart at midnight and were headed directly toward each other. If they collided at 8 a.m., find the speed of both ships if one was 20 miles per hour faster than the other. First: Draw the diagram. D 1 + D 2 = 400 R 1 T 1 + R 2 T 2 = 400T 1 = T 2 = 8R 1 = R (R )(8) + R 2 (8) = 400 The speeds of the trains were 15 and 35 mph. D1D1 D2D2 8R R 2 = R = R 2 = 240 R 2 = 15 mph R 1 = R 1 = 35 mph

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