Lessons · Quantitative Reasoning
CLT Quantitative Reasoning · Lesson
Rates and work
Distance = rate × time, and work = rate × time. When two people work together, add their rates, not their times.
- Write each rate as "jobs per hour": a job done in 3 hours is 1/3 per hour.
- Add rates for people working together.
- Time = 1 ÷ combined rate. For average speed, use total distance ÷ total time.
Q. Ann paints a fence in 3 hours and Ben in 6. Working together, how long do they take?
Answer 2 hours
1/3 + 1/6 = 1/2 fence per hour, so 2 hours. It must be less than Ann's 3 hours alone.
- Averaging the two times (4.5 hours). Together must be faster than the faster worker.
- Averaging speeds for a round trip. 30 mph out and 60 mph back averages 40 mph, not 45.
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