127
Solving rate-of-work problems (practice)
Textbook: Part 4, lesson 127, pp. 52–54
GoalSolving two-stage and two-object rate problems with a table.
New words
stage · bosqichwaste · isrofweek · haftaday (24 hours) · sutka
Explanation
If a job is done in two stages, we find the amount of work of each stage separately (A = w × t) and add them. If the rate does not change, we find the time needed for the second stage using the rate found from the first stage. We remember that a day has 24 hours.
Worked examples
A craftsman made 12 pots a day for 4 days, then 15 pots a day for 3 days. Total: 12 × 4 + 15 × 3 = 48 + 45 = 93 pots.
Gardeners mowed 450 m² of lawn in 3 hours. The rate is 450 : 3 = 150 m²/h. For another 750 m² they need 750 : 150 = 5 hours.
Class activity
“Two stages”: each child puts dots on paper for 1 minute at one speed and then for 1 minute at another speed. They find the total number of dots using a table.
Practice
1
Gardeners mowed 450 m² of lawn in 3 hours. At the same rate, in how many hours will they mow another 750 m²?
5
2
A pipe has two leaks: 5 l per hour from the first and 9 l per hour from the second. How many litres of water are wasted in one day (24 hours)?
336
3
A packer packed 40 boxes per hour for 3 hours and then 55 boxes per hour for 2 hours. How many boxes did he pack in total?
230
4
A loom works 8 hours a day and weaves 36 m of cloth per hour. How many metres does it weave in a five-day working week?
1440
5
One worker makes 7 parts per hour and another makes 9. How many parts do they make together in 6 hours?
96