1. 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

2. 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

3. 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

4. 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

5. 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
2R = 332
The rate of the first train was 101 kmph.
2R1 = 202
R1 = 101 kmph

6. 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 =
(R2 + 20)(8) + R2(8) = 400
R1 = 35 mph
8R R2 = 400
16R = 400
The speeds of the trains were 15 and 35 mph.
16R2 = 240
R2 = 15 mph