50
Moving towards each other
Textbook: Part 2, lesson 50, pp. 34–36
GoalMotion in opposite directions: separation speed.
New words
separation speed · uzoqlashish tezligiopposite directions · qarama-qarshi yo‘nalishfrom the same place · bir joydandistance between · oraliq masofa
Explanation
If two objects leave the same place at the same time in opposite directions, the distance between them grows every hour by v₁ + v₂; this is the separation speed: v_sep = v₁ + v₂. After time t the distance between them is S = (v₁ + v₂) × t. In reverse problems S : t gives the separation speed. For example, two friends walk from the school gate in opposite directions at 50 and 65 m/min: they get 115 m further apart every minute, 460 m in 4 minutes.
Worked examples
Separation speed 50 + 65 = 115 m/min; in 4 minutes 115 × 4 = 460 m.
Two buses leave a stop in opposite directions at 45 and 55 km/h: after 3 h they are (45 + 55) × 3 = 300 km apart.
Class activity
“Back to back”: in the yard (with the teacher watching) two children stand back to back and each walks 10 steps in opposite directions. The class works out the distance between them as the sum of both walks and checks it by measuring.
Practice
1
Two friends walk from one place in opposite directions at 50 and 65 m/min. What is the separation speed in m/min?
115
2
Two buses leave one stop in opposite directions at 45 and 55 km/h. How many km apart are they after 3 h?
300
3
Two cyclists leave one place in opposite directions. After 2 h they are 56 km apart. One rode at 13 km/h. What was the other's speed in km/h?
15
4
Two ships sail from one pier in opposite directions at 25 and 35 km/h. After how many hours are they 240 km apart?
4