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 school mural uses a green paint made by mixing blue and yellow paint in the ratio 2 : 3 by volume. How many liters of blue paint are needed to make 15 liters of the green paint?
- A.
  6
- B.
  7.5
- C.
  9
- D.
  10
Answer: A. 6
The ratio 2 : 3 has 5 parts, so blue is 2/5 of the mix: (2/5)(15) = 6 liters. Choice B (7.5) splits the 15 liters in half; choice C (9) is the amount of yellow; choice D (10) takes 2/3 of the total, treating the part-to-part ratio as part-to-whole.
Question 3
A city bike-share program in Medellín recorded 5,000 rides in one month. The ratio of weekday rides to weekend rides was 7 : 3. How many weekend rides were recorded?
- A.
  1,500
- B.
  1,667
- C.
  2,143
- D.
  3,500
Answer: A. 1,500
The ratio has 7 + 3 = 10 parts, so weekend rides are 3/10 of 5,000, which is 1,500. Choice B divides the total by 3; C treats 3 : 7 as a part-to-whole fraction, 3/7 of the rides; D gives the weekday rides, not the weekend rides.
Question 4
In a paper airplane contest, Imran folds 45 planes in 30 minutes and Lena folds 40 planes in 20 minutes, each at a steady rate. How many planes do the two of them fold together in 1 hour?
- A.
  85
- B.
  105
- C.
  120
- D.
  210
Answer: D. 210
Imran folds 45 ÷ 30 = 1.5 planes per minute, or 90 per hour; Lena folds 2 per minute, or 120 per hour. Together that is 90 + 120 = 210 in an hour. Choice A (85) adds the counts from the two different time periods; B (105) averages the two hourly rates; C (120) counts Lena only.
Question 5
On a walking tour in Istanbul, a guide leads a group from the Galata Tower to a spice market 3 km away, walking at 3 km/h. After a 30-minute stop at the market, the group walks back along the same route at 6 km/h. What is the group's average speed for the whole tour, including the stop, in kilometers per hour?
- A.
  1.5
- B.
  3
- C.
  4
- D.
  4.5
Answer: B. 3
The tour covers 3 + 3 = 6 km in 1 h out, 0.5 h at the market and 0.5 h back, which is 2 h, so the average speed is 6 ÷ 2 = 3 km/h. Choice A (1.5) uses only the one-way 3 km; C (4) leaves out the stop, 6 ÷ 1.5; D (4.5) averages the two walking speeds.

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