Rate Word Problems
Rate problems are about how fast things happen — how quickly a pool fills, how long two people take to finish a job together, or how many widgets a machine produces per hour. The key insight you need is that rates add when things work together and the formula rate × time = work governs everything. The classic version is two pipes filling a pool: one fills it in 3 hours, the other in 6, and you need to figure out how long they take working together. Once you see that the first pipe does 1/3 of the job per hour and the second does 1/6, you're adding fractions — and suddenly the problem is straightforward. These show up constantly in standardized tests and job aptitude exams.Find average speed when traveling different distances at different speeds. Learn why arithmetic mean fails for average speed problems.
Solve for distance when return trip is faster due to higher speed. Use distance = rate × time with two conditions.
Boat travels 325 mi with current, 265 mi against current in same time. Boat speed is 59 mph. Find current.
Find boat speed in still water and current speed. 210m round trip: downstream 10h, upstream 70h.
Find boat speed in still water given upstream/downstream times and current. Learn to set up distance equations with relative velocity.
David drives to work in 20 min, bikes in 45 min. Car speed is 4.5 mph faster. Find distance to work.
Eastbound car is 4 mph faster than westbound. Cars 208 miles apart after 2 hours. Find eastbound speed.
Find time for one worker to complete a task alone when combined and individual rates are known.
Find the time to fill a pool when two sources work together using combined work rates and reciprocals.
Find time for two workers to complete a task together using work rates. Master combined rate problems.