ACT Math Unit Conversion: 19 Practice Problems with Step-by-Step Explanations
Unit conversion problems rarely test a new math concept — they test whether you noticed that the problem gives you information in one unit (feet, hours, gallons) but asks for the answer in a different unit (inches, minutes, quarts). The math itself is usually simple arithmetic; the difficulty is entirely in keeping track of which conversion factor to multiply or divide by, and in which direction.
A reliable method is dimensional analysis: write out your starting quantity with its unit, then multiply by a conversion fraction arranged so the unit you don't want cancels out, leaving only the unit you do want. For example, converting 90 feet to yards means multiplying by (1 yard / 3 feet) — the "feet" cancels, leaving yards. On multi-step problems, it often helps to convert every given quantity into the same unit system first (all in inches, or all in minutes) before doing any other calculation, rather than trying to convert mid-calculation.
Common traps include converting in the wrong direction (multiplying instead of dividing, or vice versa), forgetting to convert a rate's time component to match a later calculation (like a rate given "per minute" when the rest of the problem is in hours), and rounding too early in a multi-step problem, which can shift the final answer enough to match a wrong (but close) answer choice. The ACT typically provides any less-common conversion factors directly in the problem, so there's rarely a need to memorize obscure conversions — just apply the ones given carefully. Work through the 19 problems below, then click to reveal each step-by-step explanation.
On this page:
- Problem 1 — Feet to inches
- Problem 2 — Hours to minutes
- Problem 3 — Feet and inches to inches
- Problem 4 — Meters to centimeters
- Problem 5 — Feet to inches
- Problem 6 — Inches to feet
- Problem 7 — Gallons to quarts
- Problem 8 — Hours to minutes
- Problem 9 — Feet to yards
- Problem 10 — Average rate over time
- Problem 11 — Minutes to hours and minutes
- Problem 12 — Square feet to acres
- Problem 13 — Rate and time to distance
- Problem 14 — Centimeters to inches
- Problem 15 — Minutes to hours
- Problem 16 — Currency conversion chain
- Problem 17 — Feet per second to miles per hour
- Problem 18 — Square feet to acres and ounces to gallons
- Problem 19 — Rotations to distance
Practice Problems
If a 6-foot giant sub is cut in half and each half is cut into quarters, how many inches long are the resulting pieces of the sub?
- A) 6
- B) 9
- C) 18
- D) 36
Convert to inches first: 6 feet × 12 inches/foot = 72 inches. Cutting in half gives two 36-inch halves.
Cutting each half into quarters gives pieces of 36/4 = 9 inches.
How many minutes would it take a car to travel 140 miles at a constant speed of 50 miles per hour?
- A) 168
- B) 117
- C) 90
- D) 64
Time in hours = distance/rate = 140/50 = 2.8 hours.
Convert to minutes: 2.8 × 60 = 168 minutes.
A piece of string that is 9 feet and 4 inches is cut into 4 equal parts. What is the length, to the nearest inch, of each part?
- A) 2 feet 1 inches
- B) 2 feet 3 inches
- C) 2 feet 4 inches
- D) 2 feet 7 inches
Convert the total length to inches: (9 × 12) + 4 = 112 inches.
Divide by 4: 112/4 = 28 inches. Convert back: 28 = 2 feet 4 inches (since 2×12=24, and 28−24=4).
Julia is wrapping packages for Christmas. If each package requires 20 centimeters of wrapping paper, what is the maximum number of packages that can be wrapped with 4 meters of wrapping paper?
(Note: 1 meter = 100 centimeters)
- A) 15
- B) 20
- C) 25
- D) 30
Convert 4 meters to centimeters: 4 × 100 = 400 centimeters.
Divide by the amount needed per package: 400/20 = 20 packages.
A 25-foot plank of wood and a 12-foot plank of wood will be cut into 10-inch pieces. How many 10-inch pieces can be cut from the two planks?
(1 foot = 12 inches)
- A) 30
- B) 37
- C) 40
- D) 44
Total plank length: 25+12 = 37 feet. Convert to inches: 37 × 12 = 444 inches.
Divide by 10: 444/10 = 44.4, so 44 whole pieces can be cut.
A category 3 hurricane rains 3 inches per hour for 36 hours. Which of the following is closest to the total feet of rain over the 36 hours?
(1 foot = 12 inches)
- A) 6
- B) 9
- C) 12
- D) 36
Total rain in inches: 3 × 36 = 108 inches.
Convert to feet: 108/12 = 9 feet.
A bakery purchases flour in 50-gallon bags. The flour is mixed with water to make loaves of bread. Each loaf of bread is made by mixing 3 quarts of flour with 2 quarts of water. What is the maximum number of loaves of bread that can be made from two 50-gallon bags of flour?
(1 gallon = 4 quarts)
- A) 66
- B) 100
- C) 133
- D) 150
Total flour: 2 × 50 = 100 gallons. Convert to quarts: 100 × 4 = 400 quarts.
Each loaf needs 3 quarts of flour: 400/3 = 133.3, so 133 whole loaves can be made (flour is the limiting ingredient).
Annabel runs 9 miles in 1 1/2 hours. What is the average number of minutes it takes her to run 1 mile?
- A) 6
- B) 10
- C) 10 1/2
- D) 13 1/2
Convert 1.5 hours to minutes: 1.5 × 60 = 90 minutes.
Divide by the number of miles: 90/9 = 10 minutes per mile.
The yarn store sells blue yarn and red yarn. Julie wants to buy 90 feet of red yarn and 45 feet of blue yarn. If red yarn sells for $2 per yard and blue yarn sells for $3 per yard, which of the following is how much Julie will pay for 90 feet of red yarn and 45 feet of blue yarn?
- A) 45
- B) 60
- C) 105
- D) 315
Convert feet to yards (1 yard = 3 feet): 90 feet = 30 yards of red, and 45 feet = 15 yards of blue.
Total cost: 30(2) + 15(3) = 60 + 45 = $105.
Prashant drove from Portland to Sacramento. At 11:00am, he was 340 miles from Sacramento. At 3:00pm, he was 95 miles from Sacramento. Which of the following values is closest to Prashant's average speed, in miles per hour, from 11:00am to 3:00pm?
- A) 61
- B) 82
- C) 85
- D) 97
Distance covered: 340−95 = 245 miles. Time elapsed: 11:00am to 3:00pm = 4 hours.
Average speed: 245/4 = 61.25, which rounds to 61.
Ming's flight was originally scheduled to depart at 6:40pm. If his flight was delayed by 436 minutes, what time did Ming's flight eventually depart?
- A) 1:24 a.m.
- B) 1:56 a.m.
- C) 2:12 a.m.
- D) 11:01 p.m.
Convert 436 minutes to hours and minutes: 436/60 = 7 hours with a remainder of 16 minutes (7×60=420, 436−420=16).
Add to the scheduled time: 6:40pm + 7 hours = 1:40am (next day), then + 16 minutes = 1:56am.
A cattle farm has a field that has a length of 600 feet and a width of 1,090 feet. Which of the following values is closest to the area, in acres, of the field?
(1 acre = 43,560 square feet)
- A) 15
- B) 210
- C) 330
- D) 218,000
Area in square feet: 600 × 1,090 = 654,000 square feet.
Convert to acres: 654,000/43,560 ≈ 15.02, closest to 15.
A car traveling at 40 mph has a leaking oil tank that is losing oil at a rate of 2 ounces per minute. How many miles will the car travel before the oil tank, which held 360 fluid ounces when it began to leak, is empty?
- A) 20.0
- B) 72.8
- C) 80.0
- D) 120.0
Time until the tank is empty: 360/2 = 180 minutes = 3 hours.
Distance traveled in that time: 40 mph × 3 hours = 120 miles.
A rectangle and a square have the same area. The length of the rectangle is 144 centimeters, and the width of the rectangle is 96 centimeters. What is the approximate length, in inches, of a side of the square?
(Note: 1 inch = 2.54 centimeters)
- A) 37.8
- B) 46.3
- C) 47.2
- D) 56.7
Rectangle's area: 144 × 96 = 13,824 square centimeters. The square's side length: √13,824 ≈ 117.58 centimeters.
Convert to inches: 117.58/2.54 ≈ 46.3.
An Olympic bicyclist broke a record during a race in the French hills. He biked 13 miles in 17 minutes. What was his average speed, to the nearest integer, in miles per hour?
- A) 4
- B) 33
- C) 46
- D) 52
Convert 17 minutes to hours: 17/60 hours.
Speed: 13/(17/60) = 13×60/17 ≈ 45.88, which rounds to 46.
One day on the foreign exchange market, 1 U.S. dollar could be exchanged for 20.3 Mexican pesos, and 1 Japanese yen could be exchanged for 0.77 U.S. dollars. On that day, which of the following is closest to how many Japanese yen could be exchanged for 50 pesos?
- A) 0.77
- B) 2.46
- C) 1.90
- D) 3.20
Convert pesos to dollars: 50 pesos ÷ 20.3 pesos/dollar ≈ 2.4631 dollars.
Convert dollars to yen: since 1 yen = 0.77 dollars, 1 dollar = 1/0.77 ≈ 1.2987 yen. So 2.4631 × 1.2987 ≈ 3.20 yen.
If it takes an object 1.5 seconds to travel 101.6 feet, to the nearest 0.01 mile per hour, what is the speed of the object?
(Note: 1 mile = 5,280 feet)
- A) 15.45
- B) 46.18
- C) 67.73
- D) 69.27
Speed in feet per second: 101.6/1.5 ≈ 67.733 ft/sec.
Convert to miles per hour: multiply by 3,600 seconds/hour, then divide by 5,280 feet/mile: 67.733 × 3,600/5,280 ≈ 46.18 mph.
Ronda will use 2.5 fluid ounces of her secret GrowthX solution on each 0.6 acres of her lettuce fields. At this rate, how much GrowthX, to the nearest gallon, will Ronda use for her 104,544 square feet of lettuce fields?
(Note: 1 acre = 43,560 square feet; 1 gallon = 128 fluid ounces)
- A) 0.013
- B) 0.028
- C) 0.047
- D) 0.078
Convert the field size to acres: 104,544/43,560 = 2.4 acres.
Find the rate per acre: 2.5/0.6 ≈ 4.1667 fluid ounces/acre. Total for 2.4 acres: 2.4 × 4.1667 ≈ 10 fluid ounces. Convert to gallons: 10/128 ≈ 0.078.
A racecar has tires with a radius of 1 foot. The racecar completes one lap of a race in 53 seconds, and the tires rotate at an average rate of 2,876 times per minute. To the closest hundredth of a mile, what is the length of the racetrack?
(1 mile = 5,280 feet)
- A) 0.96
- B) 1.51
- C) 3.02
- D) 3.42
Each tire rotation covers the tire's circumference: C = 2πr = 2π(1) ≈ 6.2832 feet.
Convert the rotation rate to a per-lap count: 2,876 rotations/min × (53/60 min) ≈ 2,540.87 rotations per lap. Total distance: 2,540.87 × 6.2832 ≈ 15,966.8 feet. Convert to miles: 15,966.8/5,280 ≈ 3.02.
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