Rates, Speed & Work
Rate formula: Rate = Distance / Time, or Rate = Work / Time
Speed problems:
If a car travels 150 miles in 3 hours, speed = 50 mph.
Average speed for a round trip: use total distance / total time, NOT the average of the two speeds.
Work problems:
If Machine A finishes a job in 4 hours, its rate = 1/4 per hour.
If Machine B finishes in 6 hours, its rate = 1/6 per hour.
Combined rate = 1/4 + 1/6 = 5/12 per hour.
Together they finish in 12/5 = 2.4 hours.
GRE trap: "If a pipe fills a pool in 3 hours and a drain empties it in 5 hours, how long to fill with both open?"
Fill rate = 1/3, Drain rate = -1/5
Net rate = 1/3 - 1/5 = 2/15. Time = 15/2 = 7.5 hours.
Reference:
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