49
Motion in opposite directions (practice)
Textbook: Part 2, lesson 49, pp. 31–33
GoalMotion in opposite directions: find an unknown speed.
New words
unknown speed · noma’lum tezlikmeeting time · uchrashish vaqticombined speed · umumiy tezlikremaining distance · qolgan masofa
Explanation
If S, the meeting time t and one speed are known, we first find the combined speed: v₁ + v₂ = S : t. Then we subtract the known speed: v₂ = S : t − v₁. For example, cyclists 90 km apart met after 3 h and one rode at 14 km/h: the combined speed is 90 : 3 = 30, so the other rode 30 − 14 = 16 km/h.
Worked examples
90 : 3 = 30 km/h combined; 30 − 14 = 16 km/h.
240 km apart, speeds 60 and 70 km/h; after 1 h the remaining distance is 240 − (60 + 70) × 1 = 110 km.
Class activity
“Hidden speed”: in pairs, one child makes up a problem and hides one speed; the partner finds it.
Practice
1
Cyclists set out towards each other from places 90 km apart and met after 3 h. One rode at 14 km/h. What was the other speed in km/h?
16
2
Two walkers 27 km apart set out towards each other and met after 3 h. One walked at 4 km/h. At what speed in km/h did the other walk?
5
3
Toshkent–Samarqand is about 300 km. Two cars set out towards each other and met after 2 h. One drove at 70 km/h. What was the other speed in km/h?
80
4
Cars set out towards each other from places 240 km apart at 60 and 70 km/h. How many km apart are they after 1 h?
110