SAT Math: Ratios, rates and units
Ratios, rates, proportional relationships and units.
- Problem-Solving and Data Analysis · Ratios, rates, proportional relationships, and units
- Both modules
- 12 practice questions
- Calculator allowed (Desmos)
What the test covers
- Unit conversion chains
- Direct proportion and scaling
Key ideas
- Unit rate = amount \(\div\) time (or per item). Scale it to the new time.
- Convert units by multiplying by a fraction equal to 1, e.g. \(\dfrac{1\text{ mile}}{1.6\text{ km}}\).
- Proportional: \(y=kx\); doubling \(x\) doubles \(y\).
Common mistakes
- Divide or multiply by the conversion factor? Check whether the answer should get bigger or smaller.
- Keep track of per-minute versus per-hour.
Do it in Desmos
The calculator is fine for the arithmetic; set the ratio up on paper first.
Worked example
Worked example
A printer prints 45 pages in 1.5 minutes. At this rate, how many pages does it print in 8 minutes?
- \(240\)
- \(180\)
- \(360\)
- \(270\)
Answer: A: \(240\)
Rate \(=45/1.5=30\) pages per minute; \(30\times8=240\).
Practice questions
Try each question before opening the solution. Desmos or your own calculator is allowed on every SAT Math question. Every answer here was re-checked independently by computer before it was published.
Question 1
Use 1 mile = 1.6 kilometers. A train travels at 72 kilometers per hour. What is its speed in miles per hour?
Show the answer and solution
Answer: 45
\(72\div1.6=45\) miles per hour.
Question 2
A machine fills 50 bottles in 2.5 minutes. At this rate, how many bottles does it fill in 8 minutes?
- \(210\)
- \(200\)
- \(160\)
- \(400\)
Show the answer and solution
Answer: C: \(160\)
Rate \(=50\div2.5=20\) bottles per minute; \(\times8=160\).
Question 3
A machine fills 36 bottles in 1.5 minutes. At this rate, how many bottles does it fill in 6 minutes?
- \(180\)
- \(216\)
- \(108\)
- \(144\)
Show the answer and solution
Answer: D: \(144\)
Rate \(=36\div1.5=24\) bottles per minute; \(\times6=144\).
Question 4
A machine fills 45 bottles in 3 minutes. At this rate, how many bottles does it fill in 8 minutes?
- \(180\)
- \(120\)
- \(360\)
- \(165\)
Show the answer and solution
Answer: B: \(120\)
Rate \(=45\div3=15\) bottles per minute; \(\times8=120\).
Question 5
A machine fills 36 bottles in 1.5 minutes. At this rate, how many bottles does it fill in 10 minutes?
- \(276\)
- \(180\)
- \(360\)
- \(240\)
Show the answer and solution
Answer: D: \(240\)
Rate \(=36\div1.5=24\) bottles per minute; \(\times10=240\).
Question 6
A machine fills 60 bottles in 4 minutes. At this rate, how many bottles does it fill in 6 minutes?
- \(150\)
- \(90\)
- \(180\)
- \(360\)
Show the answer and solution
Answer: B: \(90\)
Rate \(=60\div4=15\) bottles per minute; \(\times6=90\).
Question 7
Use 1 mile = 1.6 kilometers. A car travels at 72 kilometers per hour. What is its speed in miles per hour?
Show the answer and solution
Answer: 45
\(72\div1.6=45\) miles per hour.
Question 8
Use 1 mile = 1.6 kilometers. A car travels at 80 kilometers per hour. What is its speed in miles per hour?
Show the answer and solution
Answer: 50
\(80\div1.6=50\) miles per hour.
Question 9
Use 1 mile = 1.6 kilometers. A car travels at 120 kilometers per hour. What is its speed in miles per hour?
Show the answer and solution
Answer: 75
\(120\div1.6=75\) miles per hour.
Question 10
Use 1 mile = 1.6 kilometers. A car travels at 96 kilometers per hour. What is its speed in miles per hour?
Show the answer and solution
Answer: 60
\(96\div1.6=60\) miles per hour.
Question 11
Use 1 mile = 1.6 kilometers. A car travels at 88 kilometers per hour. What is its speed in miles per hour?
Show the answer and solution
Answer: 55
\(88\div1.6=55\) miles per hour.
Keep going
- Previous topic: Nonlinear functions
- Next topic: Percentages
- All SAT Math skills · Adaptive SAT Math module simulator · Official SAT practice (Bluebook, Khan Academy)
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