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Ratios, rates, proportional relationships, and units — SAT practice questions

Ratios, rates, proportional relationships, and units on SAT Math asks students to convert units, set up direct or inverse proportions, and apply rates in distance-speed-time situations. A student must keep units consistent, write the correct relationship, and solve for one unknown. Items are typically short word problems, such as converting miles to yards, finding time when it is inversely proportional to speed, or determining when two trains traveling toward each other meet. Traps include mismatched units, treating inverse variation as direct, and combining speeds the wrong way. Answer choices are usually a single numeric value, and some items require a student-produced response.

  • Section: Math 44 questions on the paper
  • 106 practice questions in the app

Sample questions

Question 1

A trail is 2.5 miles long. How long is the trail, in yards? (1 mile =1,760=1{,}760 yards)

  1. A704
  2. B1,7601{,}760
  3. C4,4004{,}400
  4. D17,60017{,}600
Show answer

Answer: C — 4,4004{,}400

2.5×1,760=4,4002.5\times1{,}760=4{,}400 yards.

Question 2

The time tt, in hours, needed to travel a fixed distance is inversely proportional to the speed ss, in miles per hour. If t=4t=4 when s=30s=30, what is the value of tt when s=24s=24?

  1. A3.2
  2. B4.8
  3. C5
  4. D6.25
Show answer

Answer: C — 5

Since tt is inversely proportional to ss, ts=4×30=120ts=4\times30=120. When s=24s=24, t=120/24=5t=120/24=5.

Question 3

Two trains start 270 miles apart and travel toward each other. One train travels at 55 miles per hour, and the other travels at 35 miles per hour. How many hours will it take for the two trains to meet?

  1. A1.5
  2. B3
  3. C4.9
  4. D7.7
Show answer

Answer: B — 3

Combined closing speed =55+35=90=55+35=90 miles per hour. Time to meet =270/90=3=270/90=3 hours.

Practice 106 Ratios, rates, proportional relationships, and units questions in the app

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