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 time for two workers to complete a task together using work rates. Master combined rate problems.
Two workers with different rates work together. Find time to complete job using combined rate method.
Find when two conveyor lines fill equal barrels using linear equations and work rates.
Solve the classic distance problem: same distance at two speeds. Find time at 80 kph given 6 hours at 60 kph.
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 machine B's time to produce 800 nails given combined rate. Solve using work rate equations with two unknowns.
Find plane airspeed and wind speed from two trips: 525 mi in 3 hr against wind, return in 2.5 hr with wind.
Find plane speed in still air and wind speed using tailwind/headwind conditions. Two-equation system solved step-by-step.
Find wind speed when a plane flies 500 mi with wind in same time as 300 mi against wind. Algebraic distance equation.