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.
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 Drill
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 :
Step 2: Calculate the Total Work Rate for 3 Seed Drills
On the second day, there are 3 seed drills. The total work rate is:
Step 3: Calculate the Area Sown in 8 Hours
Using the total work rate, the area sown in 8 hours is:
Final Answer:
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 Drill
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:
Total work rate of 2 seed drills = Area sown/Time taken = 7 ha/5 hours = 1.4 ha/hour.
Since there are 2 seed drills:
2r = 1.4 ha/hour.
Solve for r :
r = 1.4/2 = 0.7 ha/hour.
Step 2: Calculate the Total Work Rate for 3 Seed Drills
On 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 Hours
Using 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:
- planimetrics
- area of a shape
- basic functions
- ratio
- inverse proportion
- direct proportionality
- simple proportion
Units of physical quantities:
Grade of the word problem:
We encourage you to watch this tutorial video on this math problem: video1
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