51
Opposite motion: mixed problems
Textbook: Part 2, lesson 51, pp. 37–39
GoalMixed problems on motion in opposite directions.
New words
moving apart · uzoqlashishapproaching · yaqinlashishmixed problem · aralash masalanumber ray · sonli nur
Explanation
In opposite-motion problems we first decide whether the objects are approaching or moving apart. In both cases the speeds add up. If the objects start S₀ apart and move away from each other, after time t the distance is S₀ + (v₁ + v₂) × t; if they approach, it is S₀ − (v₁ + v₂) × t. On a number ray it is the same: if A(2) and B(50) approach at 3 and 5 unit segments per second, they meet after (50 − 2) : (3 + 5) = 6 s.
Worked examples
Cyclists leave villages 30 km apart, riding away from each other at 12 and 15 km/h: after 4 h they are 30 + (12 + 15) × 4 = 138 km apart.
160 km apart, 18 and 22 km/h, after 3 h: 160 − (18 + 22) × 3 = 40 km.
Class activity
“Closer or further?”: the teacher reads problems, children show with hand signs (closer / further) and then solve.
Practice
1
Two ships sail from one pier in opposite directions at 40 and 50 km/h. After how many hours are they 450 km apart?
5
2
Two cyclists leave villages 30 km apart and ride away from each other in opposite directions at 12 and 15 km/h. How many km apart are they after 4 h?
138
3
Cyclists set out from places 160 km apart at 18 and 22 km/h towards each other. How many km apart are they after 3 h?
40
4
On a ray A(2) and B(50) move towards each other at 3 and 5 unit segments per second. What is the coordinate of the meeting point?
20