Seed drills
The tractor driver connected two seed drills behind the tractor and sowed 7 ha of grain in 5 hours. How many hectares did he plant in 8 hours the next day if he connected three seed drills?
Correct answer:
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Dr. Math
To solve this problem, we will use the concept of work rate. The work rate is the amount of work done per unit of time. Here, the work is sowing grain, measured in hectares (ha), and the time is measured in hours.
1. On the first day:
- Number of seed drills: 2.
- Area sown: 7 ha.
- Time taken: 5 hours.
2. On the second day:
- Number of seed drills: 3.
- Time taken: 8 hours.
The work rate of one seed drill is the amount of area it can sow per hour. Let r be the work rate of one seed drill in ha/hour.
From the first day:
Since there are 2 seed drills:
Solve for r :
On the second day, there are 3 seed drills. The total work rate is:
Using the total work rate, the area sown in 8 hours is:
The tractor driver planted:
Given:
1. On the first day:
- Number of seed drills: 2.
- Area sown: 7 ha.
- Time taken: 5 hours.
2. On the second day:
- Number of seed drills: 3.
- Time taken: 8 hours.
Step 1:
Calculate the Work Rate of One Seed DrillThe work rate of one seed drill is the amount of area it can sow per hour. Let r be the work rate of one seed drill in ha/hour.
From the first day:
Total work rate of 2 seed drills = Area sownTime taken = 7 ha5 hours = 1.4 ha/hour.
Since there are 2 seed drills:
2r = 1.4 ha/hour.
Solve for r :
r = 1.42 = 0.7 ha/hour.
Step 2:
Calculate the Total Work Rate for 3 Seed DrillsOn the second day, there are 3 seed drills. The total work rate is:
Total work rate = 3r = 3 × 0.7 = 2.1 ha/hour.
Step 3:
Calculate the Area Sown in 8 HoursUsing the total work rate, the area sown in 8 hours is:
Area sown = Total work rate × Time = 2.1 × 8 = 16.8 ha.
Final Answer:
The tractor driver planted:
16.8 ha
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You need to know the following knowledge to solve this word math problem:
planimetricsbasic operations and conceptsUnits of physical quantitiesGrade of the word problem
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