119
Solving movement problems
Textbook: Part 4, lesson 119, pp. 28–30
GoalSolve movement problems with diagrams and tables; two-stage journeys.
New words
diagram · sxematable · jadvalstage · bosqichto arrive · yetib borish
Explanation
It helps to write the condition in a table with columns v, t and s. If the journey has two stages, find the distance of each stage separately and then add. To compare two movements, keep one quantity the same (for example the distance) and compare the times or the speeds.
Worked examples
A car drove 3 hours at 50 km/h and then 2 hours at 70 km/h. Stage 1: 50 × 3 = 150 km, stage 2: 70 × 2 = 140 km. Total 150 + 140 = 290 km.
Tashkent–Samarkand is about 300 km. A bus at 60 km/h takes 300 : 60 = 5 hours, at 75 km/h it takes 300 : 75 = 4 hours, which is 1 hour faster.
Class activity
“Fill the table”: the teacher tells a short story about a journey; children draw a v, t, s table in their notebooks, write the known numbers and find the unknown.
Practice
1
The distance between two stations is 168 km. How many hours does a train going 56 km/h need to get from one to the other?
3
2
A traveller rode a horse at 7 km/h for 2 hours and then walked at 3 km/h for 4 hours. How many km did he cover in total?
26
3
Two cyclists ride 120 km. The first goes 15 km/h, the second 20 km/h. How many hours earlier does the second one arrive?
2
4
It is 2 km 400 m from home to the orchard. Grandad walks at 80 m/min. In how many minutes does he reach the orchard?
30