Solving Rate Problems and Applied Mathematics
Solving Rate Problems
6E Solving Rate Problems
Exercise 6E
FLUENCY
Example 13a 1: Geoff can type 30 words per minute.
Part a: Determine how many words he can type in 4 minutes.
Calculation: 30 words/minute × 4 minutes = 120 words
Part b: Determine how many words he can type in 10 minutes.
Calculation: 30 words/minute × 10 minutes = 300 words
Example 13a 2: A factory produces 40 plastic bottles per minute.
Part a: Calculate how many bottles the factory can produce in 60 minutes.
Calculation: 40 bottles/minute × 60 minutes = 2400 bottles
Part b: Calculate how many bottles the factory can produce in an 8-hour day of operation.
Calculation: 40 bottles/minute × 480 minutes (8 hours × 60 minutes) = 19200 bottles
Example 13b: Instructions for scenario-based problems with detailed calculations.
Problem 3: Mario is a professional home painter. He uses an average of 2 litres of paint per hour.
Calculation for 40 hours: 2 litres/hour × 40 hours = 80 litres
Problem 4: A truck travels 7 km per litre of fuel.
Required calculation: To determine how much fuel is needed for 280 km.
Calculation: 280 km ÷ 7 km/litre = 40 litres
Problem 5: Daniel practises his guitar for 40 minutes every day.
Determine how many days to log 100 hours of practice.
Total minutes in 100 hours: 100 hours × 60 minutes/hour = 6000 minutes
Days required: 6000 minutes ÷ 40 minutes/day = 150 days
Problem 6: A flywheel rotates at a rate of 1500 revolutions per minute.
Part a: Calculate total revolutions in 15 minutes.
Calculation: 1500 revolutions/minute × 15 minutes = 22500 revolutions
Part b: Calculate revolutions in 15 seconds.
Calculation: (1500 revolutions/minute ÷ 60 seconds/minute) × 15 seconds = 375 revolutions
Part c: Determine how long it takes to complete 15000 revolutions.
Time Calculation: 15000 revolutions ÷ 1500 revolutions/minute = 10 minutes
Part d: Determine how long it takes to complete 150 revolutions.
Time Calculation: 150 revolutions ÷ 1500 revolutions/minute = 0.1 minutes or 6 seconds
Problem 7: Putra is an elite rower with a heart rate of 125 beats per minute (bpm) during training and a resting heart rate of 46 bpm.
Part a: Calculate heartbeats during a 30-minute workout.
Calculation: 125 bpm × 30 minutes = 3750 beats
Part b: Calculate heartbeats during 30 minutes of rest.
Calculation: 46 bpm × 30 minutes = 1380 beats
Part c: If his coach suggests he stops after 10000 beats, determine training duration.
Time Calculation: 10000 beats ÷ 125 bpm = 80 minutes
PROBLEM-SOLVING
Problem 8: Cost of paving a driveway that is 18 m long and 4 m wide at $35 per square metre.
Area Calculation: 18 m × 4 m = 72 square metres
Total Cost: 72 square metres × $35/square metre = $2520
Problem 9: A saltwater swimming pool requires 2 kg of salt per 10000 litres of water. Dimensions: 1.5 m deep, 5 m wide, 15 m long.
Volume Calculation: 1.5 m × 5 m × 15 m = 112.5 cubic metres = 112500 litres
Salt Requirement: (112500 litres ÷ 10000 litres) × 2 kg = 22.5 kg
Problem 10: The Bionic Woman gives Batman a 12-second start in a 2 km race, running rates are 5 km/min and 3 km/min.
Time Calculation for Batman: Distance = Speed × Time → Time = Distance/Speed
Batman's time: 2000 m ÷ (3 km/min) = 666.67 seconds
Bionic Woman's time: 2000 m ÷ (5 km/min) = 400 seconds
Winner Calculation: The Bionic Woman's advantage is the 12-second head start.
Batman's total time: 666.67 seconds + 12 seconds = 678.67 seconds
Conclusion: Bionic Woman wins by: 678.67 seconds - 400 seconds = 278.67 seconds
Problem 11: At a school camp, enough food for 150 students lasts 5 days.
Part a: Determine how much longer the food lasts for 100 students.
Calculation: Total food = 150 × 5 = 750 student-days
Days food lasts = 750 student-days ÷ 100 students = 7.5 days
Part b: If food runs out after 4 days, determine how many students were present.
Students Calculation: Total food = 150 × 5 = 750 food units
Students in 4 days = 750 food units ÷ 4 = 187.5 students (approximately 188 students)