Teacher Real World Robots
Autonomous Harvester / Productivity
Note to the teacher
In this page, students will solve problems involving mathematical operations, averages, fractions, percentages and unit
conversions. Students will determine speed and area based on rate, and compare different speeds and areas as fractions
and percentages. Students are expected to apply prior knowledge in all these areas, though they are given a formula to
convert square meters to square feet. Teachers may wish to review any or all of these skills depending on their students’
background. Students will also learn an important advantage of robots over driven work vehicles. Their productivity does
not drop off due to driver fatigue.
Instructions
The autonomous harvester pictured below is able to work more efficiently than a conventional machine because it never
slows down due to driver fatigue. Use this information to answer the questions below.
Foot2
1
Meter2
=
.093
The autonomous harvester uses a kind of
line tracking program to harvest.
1. The autonomous harvester maintains its top speed of 4 miles per hour for all 8 hours it works.
A conventional harvester went 4 miles per hour for the first 4 hours, then went 25% slower than
4 miles per hour for 4 hours.
– How fast did the conventional harvester go in the second 4 hours?
– What was the average speed of the conventional harvester for the entire 8 hours?
– What fraction of the speed of the autonomous harvester did the conventional harvester go?
– What percentage of the speed of the autonomous harvester did the conventional harvester go?
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©2005 Robomatter Inc. RE 2.5_RW 1.1
Real World Robots Teacher
Autonomous Harvester / Productivity
Students are expected to use the following procedure:
• Identify what information is requested in the question
• Apply previous knowledge of arithmetic, fractions and percentages to find the answer in square feet
• Use the unit conversion formula provided to convert the answer into feet, if necessary
Approximate classroom time: 10-20 minutes depending on students’ background
Students successfully completing the worksheet will be able to:
1. Explain one advantage robots have over driven vehicles: that their productivity does not
2.
3.
4.
5.
lessen due to driver fatigue
Compute area and distance based on rate
Convert between fractions and percentages
Perform various mathematical operations
Multiply decimals and fractions
Standards addressed
Math Standards
Numbers and Operations
Algebra
Geometry
Measurement
Problem Solving
Technology Standards
The Nature of Technology Standards 1; Design 8, 9
Note: Workbook answers begin on the next page.
©2005 Robomatter Inc. RE 2.5_RW 1.1
7.6
Teacher Real World Robots
Autonomous Harvester / Productivity
Instructions
The autonomous harvester pictured below is able to work more efficiently than a conventional machine because it never
slows down due to driver fatigue. Use this information to answer the questions below.
Foot2
1
Meter2
=
.093
The autonomous harvester uses a kind of
line tracking program to harvest.
1. The autonomous harvester maintains its top speed of 4 miles per hour for all 8 hours it works.
A conventional harvester went 4 miles per hour for the first 4 hours, then went 25% slower than
4 miles per hour for 4 hours.
– How fast did the conventional harvester go in the second 4 hours?
To find out how fast the conventional harvester went in the second 4 hours, you first need to find what speed
is 25% slower than 4 miles per hour. To find 25% of 4, convert the percentage to a fraction by multiplying it by
1/100%. So 1/100% x 25% = .25. Now multiply .25 by 4. So .25 x 4 = 1. So if it goes 25% slower, it is going (4-1)
miles per hour, or 3 miles per hour.
– What was the average speed of the conventional harvester for the entire 8 hours?
To determine the average speed of the conventional harvester, find the total distance it travelled and divide it by
the total hours it worked. So the total distance equals (4 miles/hour x 4 hours) + (3 miles/hour x 4 hours)
= 28 miles. Divide this by the total hours, 8, and you will see that the average speed is 28 miles/8hours = 3.5
miles per hour.
– What fraction of the speed of the autonomous harvester did the conventional harvester go?
We can see that the robotic harvester travelled 8 hours x 4 miles per hour, or 32 miles. The fraction would equal
(28 miles)/(32 miles) = 7/8 ths.
– What percentage of the speed of the autonomous harvester did the conventional harvester go?
The percentage equals the fraction multiplied by 100. So 7/8 x 100 = 87.5%
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©2005 Robomatter Inc. RE 2.5_RW 1.1
Real World Robots Teacher
Autonomous Harvester / Productivity
2. The autonomous harvester goes 4 miles per hour for all 8 hours it works.
A conventional harvester went 3.5 miles per hour for the first 6 hours, then 2.5 miles per hour for the last 2 hours.
– How far did the autonomous harvester travel in 8 hours?
To find how far the autonomous harvester travelled in 8 hours, multiply its miles per hour by the number of hours
it worked. So: 4 miles/hour x 8 hours = 32 miles.
– How far did the conventional harvester travel in 8 hours?
To find how far the conventional harvester travelled in 8 hours, multiply its miles per hour by the number of hours it
worked. So: (3.5 miles/hour x 6 hours) + (2.5 miles/hour x 2 hours) = 21 miles + 5 miles = 26 miles.
– What fraction of the distance the autonomous harvester travelled did the conventional harvester travel?
The fraction would equal (26 miles)/(32 miles) = 13/16ths.
– What percentage of the distance the autonomous harvester travelled did the conventional harvester travel?
The percentage equals the fraction multiplied by 100. So 13/16 x 100 = 81.25%.
3. The autonomous harvester harvests 300,000 square feet per hour for all 8 hours it works.
A conventional harvester harvests 250,000 square feet per hour for the first 7 hours, then
150,000 square feet for the last hour.
– How many square meters did the autonomous harvester harvest in 8 hours?
To find what area the autonomous harvester harvested in 8 hours, multiply its square feet per hour by the number
of hours it worked. So 300,000 ft2/hour x 8 hours = 2,400,000 ft2. To convert this to square meters, just multiply it
by the conversion factor = 2,400,000 ft2 x .09 ft2/m2 = 216,000m2.
– How many square meters did the conventional harvester harvest in 8 hours?
To find what area in square feet the autonomous harvester harvested in 8 hours, multiply its square feet per hour by
the number of hours it worked. So (250,000 ft2/hour x 7 hours) + (150,000 ft2/hour x 1 hour) = 1,900,000 ft2. To convert this to square meters, use the conversion factor at the top of page 1. So 1,900,000 ft2 x .093 m2/ft2 = 176,700 m2.
– What fraction of the area the autonomous harvester cut did the conventional harvester cut?
The fraction would equal (1,900,000 ft2)/(2,400,000 ft2) = 19/24ths.
– What percentage of the area the autonomous harvester cut did the conventional harvester cut?
The percentage equals the fraction multiplied by 100. So 19/24 x 100 = 79.17%.
NAME
©2005 Robomatter Inc. RE 2.5_RW 1.1
DATE
7.8