Scenario: Work Efficiency & Speed - Learn to identify and solve direct and inverse proportion problems!
A typist can type 4000 words per hour. How many words can they type in 3.5 hours?
Solution: 4000 words/hour × 3.5 hours = 14,000 words
This is a direct proportion: more time = more words typed.
Direct Proportion: y = kx (where k is the constant of proportionality)
As x increases, y increases proportionally. The ratio y/x remains constant.
A car travels 300 km. If it travels at 60 km/h, it takes 5 hours. How long would it take at 75 km/h?
Solution: Distance = Speed × Time
300 km = 75 km/h × Time
Time = 300 ÷ 75 = 4 hours
This is an inverse proportion: higher speed = less time needed.
Inverse Proportion: y = k/x (where k is the constant)
As x increases, y decreases proportionally. The product x × y remains constant.
• Straight line through origin
• Positive slope
• y increases as x increases
• Hyperbola (curved line)
• Never touches axes
• y decreases as x increases
A machine produces 120 items in 2 hours. How many items can it produce in 7 hours?
Your solution:
6 workers can complete a job in 8 days. How many days would it take 12 workers?
Your solution: