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 kayak speed and current velocity using upstream/downstream distances and times. System of equations application.
Solve round-trip problems where the same route is traveled at different speeds. The slower trip takes longer.
Solve this relative speed word problem: car chases truck with head start. Find catch-up time using distance = rate × time.
Faucet A fills in 2 hours, Faucet B in 3 hours. Find time for both together using work rates.
OfficeJet copies dissertation in 10 min, LaserJet in 16 min. How long working together?
Two trains travel 330km at different speeds, one taking 30 min less. Solve for both speeds using distance-rate-time equations.
Find when two trains traveling toward each other will meet. Combined rate and distance formula.
Train leaves Boston at 4pm; second train at 8pm, 84 mph faster. Find both speeds when second overtakes first at 10pm.
Samantha swims upstream 1 hour, downstream 12 min same distance. River current 4 mph. Solve for swimming speed.
Worker alone takes 10 hours. With assistant, 6 hours. Find assistant's solo time using work-rate equations.