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.
David drives to work in 20 min, bikes in 45 min. Car speed is 4.5 mph faster. Find distance to work.
Find time for two workers to complete a task together using work rates. Master combined rate problems.
Find when two conveyor lines fill equal barrels using linear equations and work rates.
Whitney drives 7 miles, mother drives 8 miles 5 mph faster, arrive simultaneously. Find Whitney's speed using distance-rate-time.
Eudora ran 12 km/h, then flew 76 km/h, total 120 km in 2 hours. Find time spent running vs. flying using system of equations.
Find plane speed in still air and wind speed using tailwind/headwind conditions. Two-equation system solved step-by-step.
Solve a work-rate problem with two pump types. Find how long 4 large + 4 small pumps fill a pool.
Chris rinses 720 dishes in 72 min, Bill in 144 min. Find time working together using work-rate formula.
Solve this relative speed word problem: car chases truck with head start. Find catch-up time using distance = rate × time.