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.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 plane speed in still air and wind speed using tailwind/headwind conditions. Two-equation system solved step-by-step.
Chris rinses 720 dishes in 72 min, Bill in 144 min. Find time working together using work-rate formula.
Faucet A fills in 2 hours, Faucet B in 3 hours. Find time for both together using work rates.
$20/hr carpenter, $25/hr blacksmith. Worked 30 hours total, earned $690. Find hours at each job.
Two trains travel 330km at different speeds, one taking 30 min less. Solve for both speeds using distance-rate-time equations.
Solve a work-rate problem where an older computer takes twice as long as a newer one. Find individual times.