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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.
Two Trains Problem: Rate and Time
Train leaves Boston at 4pm; second train at 8pm, 84 mph faster. Find both speeds when second overtakes first at 10pm.
Upstream-Downstream Swimming: Find Speed in Still Water
Samantha swims upstream 1 hour, downstream 12 min same distance. River current 4 mph. Solve for swimming speed.
Work Rate Problem: Parking Lot
Worker alone takes 10 hours. With assistant, 6 hours. Find assistant's solo time using work-rate equations.
Work Rate Problem: Two Computers Email
Solve a work-rate problem where an older computer takes twice as long as a newer one. Find individual times.
Work Rate Problem | Staggered Start Printers
Two printers: larger finishes in 40 min, smaller takes 50 min after larger breaks. Find smaller printer's solo time.
Work Rate: Staggered Machine Start
One copier works alone 5 min, then two machines work together. Calculate total time to finish using work-rate equations.