ACT · Math · Integrating Essential Skills

Rates, ratios, and proportions

Rates, ratios, and proportions is part of Integrating Essential Skills in the ACT Math section. The questions below are written in the style of the real test, each with the answer and a worked explanation.

Question types you will see here include scale a quantity by proportion, unit conversion chain, map scale and model scale and combined work rate.

Common traps: setting up the proportion inverted; adding the difference instead of scaling; rounding in the middle of the work.

Sample questions

Question 1
A train travels 12 miles in 2 hours at a constant speed. At this rate, how many miles would it cover in 3 hours?
- A.
  8
- B.
  15
- C.
  18
- D.
  36
Answer: C. 18
The rate is 12 ÷ 2 = 6 miles per hour. In 3 hours: 6 × 3 = 18.
Question 2
A family's car used 6.4 gallons of gasoline for a trip from Houston to San Antonio at 35 miles per gallon. At 28 miles per gallon, how many gallons would the same trip require?
- A.
  5.12
- B.
  6.4
- C.
  8
- D.
  224
Answer: C. 8
The trip is 6.4 × 35 = 224 miles. At 28 mpg it needs 224 ÷ 28 = 8 gallons. Lower fuel economy means more gallons for a fixed distance. Choice A (5.12) scales the gallons directly with the miles per gallon. Choice B (6.4) assumes the gallons do not change. Choice D (224) gives the trip distance in miles, not gallons.
Question 3
A rooftop in Muscat has 48 solar panels of two types in the ratio 5 : 7. Each Type 1 panel produces 0.3 kW and each Type 2 panel produces 0.5 kW at midday. What is the total midday output, in kW?
- A.
  18.4
- B.
  19.2
- C.
  20
- D.
  24
Answer: C. 20
Each part is 48 ÷ 12 = 4 panels: 20 of Type 1 and 28 of Type 2. Output = 20(0.3) + 28(0.5) = 6 + 14 = 20 kW. Choice A (18.4) reverses the ratio, giving 28 Type 1 and 20 Type 2 panels. Choice B (19.2) averages the two outputs and applies 0.4 kW to all 48 panels. Choice D (24) gives all 48 panels the larger 0.5 kW output.
Question 4
An artist's sketch of a mural measures 2 meters by 0.8 meter and uses 90 milliliters of paint. The finished mural is 12 meters by 4.8 meters, and the paint needed is proportional to area. How many liters of paint does the finished mural need?
- A.
  0.54
- B.
  3.24
- C.
  19.44
- D.
  32.4
Answer: B. 3.24
Every length is multiplied by 6, so the area is multiplied by 36 and the paint is 90 × 36 = 3,240 mL, which is 3.24 liters. Choice A (0.54) multiplies by the length ratio 6 instead of the area ratio 36; Choice C (19.44) multiplies by 6³; Choice D (32.4) is off by a factor of 10.
Question 5
A bakery in Cairo blends two flours, one with 10% protein and one with 15% protein, to make 60 kg of flour that is 12% protein. How many kilograms of the 15% flour are needed?
- A.
  12
- B.
  24
- C.
  30
- D.
  36
Answer: B. 24
With x kg of 15% flour: 0.15x + 0.10(60 − x) = 0.12(60), so 0.05x = 1.2 and x = 24 kg. A divides the 2-point gap by 10 instead of the 5-point spread. C assumes equal parts. D is the amount of the 10% flour, 60 − 24, not the 15% flour.

Find your real gaps

A few questions show the style. The free scan shows which ACT skills cost you the most points, then builds a plan around them.

Take the free scan