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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.
Combined Work Rate Problem
Find time for two workers to complete a task together using work rates. Master combined rate problems.
Two Jobs Hourly Rate System of Equations
$20/hr carpenter, $25/hr blacksmith. Worked 30 hours total, earned $690. Find hours at each job.
Train Speed Problem
Two trains travel 330km at different speeds, one taking 30 min less. Solve for both speeds using distance-rate-time equations.