"Rates, Ratios, and Proportions" are a major part of the SAT Math section. This guided path will teach you the core frameworks for solving "work" problems, a common real-world scenario tested on the exam.
Start with the fundamental principle: converting a total time to complete a job into a rate of work per unit of time (e.g., per hour or day).
Don't add times directly! Convert to Rate (Work per 1 Day).
Takes 10 Days
Takes 15 Days
Rate = 1 / Time
A's Rate: $$ \frac{1}{10} $$ job/day
B's Rate: $$ \frac{1}{15} $$ job/day
Add fractions:
$$ \frac{1}{10} + \frac{1}{15} = \frac{3}{30} + \frac{2}{30} = \frac{5}{30} = \frac{1}{6} $$Together, they do 1/6 of the job per day.
Flip the combined rate back to time.
$$ \text{Time} = \frac{1}{\text{Rate}} = \frac{1}{1/6} = \mathbf{6 \text{ Days}} $$Learn how to handle common scenarios with opposing forces, like a draining pipe, by simply using a negative rate.
A drain works against the filling pipes. Treat its rate as Negative.
A: $$ +\frac{1}{12} $$
B: $$ +\frac{1}{18} $$
C: $$ -\frac{1}{24} $$
Flip the net rate:
$$ \text{Time} = \frac{72}{7} \approx \mathbf{10.28 \text{ Hours}} $$Use the concept of "Total Effort" as a powerful shortcut for problems involving groups of workers.
For groups, calculate Total Effort (Men × Days). This total is constant.
"A project requires 25 people to complete it in 8 days."
If we only have 20 workers?
$$ 20 \times D = 200 $$If we must finish in 5 days?
$$ M \times 5 = 200 $$Learn the step-by-step process of translating a real-world SAT word problem into a solvable algebraic model using the Work = Rate × Time formula.
Build the model: $$ \text{Work} = \text{Rate} \times \text{Time} $$
A pipe fills a tank at rate 'r'. Tank capacity is 200. It is already 1/4 full. Write equation for time 'h' to fill the rest.
Tank is 1/4 full, so we need to fill 3/4.
$$ \text{Work} = \frac{3}{4} \times 200 = 150 $$Rate = r
Time = h
Put your understanding of SAT Work Rate Problems: A Guide to Real-World Modeling to the test with our premium, adaptive practice questions. Build pacing efficiency and eliminate knowledge gaps now.
