29
Work problems
Textbook: Part 1, lesson 29, pp. 112–113
GoalKnow the relation A = N · t between work done, productivity and time; solve joint-work problems.
New words
productivity (rate of work) · mehnat unumdorligiwork done · bajarilgan ishtime · vaqtworking together · birgalikda ishlash
Explanation
The work done in one unit of time is called productivity. The amount of work is A = N · t: multiply productivity by time. From it N = A : t and t = A : N follow. If two people work together, their productivities add: first find each one's work per day, add them, then divide the whole job by that sum. The amount of work must always be measured in the same unit (items, pages, hectares).
Worked examples
A worker making 14 parts an hour makes A = 14 × 6 = 84 parts in 6 hours. If 144 parts are made in 6 hours, N = 144 : 6 = 24 parts per hour.
Zafar makes 300 parts in 10 days and Nodir in 15 days. Per day: 300 : 10 = 30 and 300 : 15 = 20; together 30 + 20 = 50; time 300 : 50 = 6 days.
Class activity
“Work table”: pupils count the words they write in 1 minute, fill a table for 5 and 10 minutes and find how long 120 words would take.
Practice
1
A printer prints 9 pages a minute. How many pages in 8 minutes?
72
2
A worker processed 144 parts in 6 hours. How many parts per hour?
24
3
A student writes a 96-page work at 12 pages a day. In how many days is it finished?
8
4
Mubina does 360 stitches in 12 days and Maryam in 24 days. In how many days do they finish together? How did you find it?
8 days: 30 + 15 = 45 per day, and 360 : 45 = 8.