Uniform Motion Problems of the Form D1 +D2 = N Lesson 94 Uniform Motion Problems of the Form D1 +D2 = N LESSON PRESENTATION Example 94.1 Example 94.2 Example 94.3

Uniform Motion D1 = D2 and R1 T1 = R2 T2 The uniform motion problems we worked earlier (Lesson 92) were about equal distances. The diagrams representing that motion are below. (a) D1 D2 (b) D1 D2 D1 = D2 and R1 T1 = R2 T2

Uniform Motion D1 + D2 = N and R1 T1 + R2 T2 = N 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. D1 D2 D1 D2 D1 + D2 = N and R1 T1 + R2 T2 = N

Example 94.1 DS DN DS + DN = 352 RS TS + RN TN = 352 TS = 5 TN = 3 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. DS DN First: Draw the diagram. DS + DN = 352 RS TS + RN TN = 352 TS = 5 TN = 3 RS = RN RS (5) + RS (3) = 352 8RS = 352 The buses were traveling at a rate of 44 kmph. RS = 44 kmph

Example 94.2 D1 D2 D1 + D2 = 332 R1 T1 + R2 T2 = 332 T1 = T2 = 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. D1 D2 First: Draw the diagram. D1 + D2 = 332 R1 T1 + R2 T2 = 332 T1 = T2 = 2 R2 = 65 R1 = ??? R1 (2) + (65) (2) = 332 2R1 + 130 = 332 The rate of the first train was 101 kmph. 2R1 = 202 R1 = 101 kmph

Example 94.3 D1 D2 D1 + D2 = 400 R1 T1 + R2 T2 = 400 T1 = T2 = 8 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. D1 D2 First: Draw the diagram. D1 + D2 = 400 R1 T1 + R2 T2 = 400 T1 = T2 = 8 R1 = R2 + 20 R1 = 15 + 20 (R2 + 20)(8) + R2(8) = 400 R1 = 35 mph 8R2 + 160 + 8R2 = 400 16R2 + 160 = 400 The speeds of the trains were 15 and 35 mph. 16R2 = 240 R2 = 15 mph