Ratios and rates (ratio tables, unit rate) Transitional Reasoning Download PDF
19 Math practice questions on Ratios and rates (ratio tables, unit rate). Questions that build towards applied reasoning.
Questions
- 1.
A commercial greenhouse operates an automated misting system that mixes liquid nutrient concentrate with water at a constant rate. According to the system's log, 18 milliliters of concentrate are mixed with 24 liters of water, 45 milliliters of concentrate with 60 liters of water, and 81 milliliters of concentrate with 108 liters of water. If the manager needs to prepare a full tank containing 180 liters of water at this exact ratio and the concentrate is sold only in 25-milliliter bottles, what is the minimum number of these bottles that must be purchased to have enough concentrate?
- 2.
A wetland conservation team uses a ratio table to monitor an electric pump that drains water from a retention basin at a constant rate, recording 72 cubic meters in 4 hours, 126 cubic meters in 7 hours, and 198 cubic meters in 11 hours. Meanwhile, an inlet stream continuously adds water into the basin at a constant rate of 6 cubic meters per hour. If the basin initially contains 456 cubic meters of water, how many hours will it take for the volume of water to decrease to exactly 120 cubic meters?
- 3.
A commercial print shop uses a ratio table to track the shipping mass of uniform boxes of cardstock. According to the shop's log, 15 boxes have a mass of 72 kilograms, 25 boxes have a mass of 120 kilograms, and 40 boxes have a mass of 192 kilograms. A delivery van with a maximum cargo weight limit of 850 kilograms is already loaded with 274 kilograms of printing equipment. What is the maximum number of these boxes of cardstock that can be added to the van without exceeding its weight limit?
- 4.
A botanical nursery prepares a specialized potting mix by combining coarse perlite and organic peat at a constant rate. According to the nursery's mixing log, 18 liters of perlite require 45 liters of peat, 30 liters of perlite require 75 liters of peat, and 42 liters of perlite require 105 liters of peat. A horticulturist has 64 liters of perlite and 150 liters of peat in storage and prepares as much potting mix as possible following this exact ratio. How many liters of perlite remain unused once the other ingredient is completely consumed?
- 5.
A municipal environmental agency purchases liquid water-testing reagent from two authorized chemical suppliers that each price their product at a constant rate. Supplier 1 records its pricing schedule in a ratio table, charging 108 for 24 liters, and 108 for 18 liters. If the agency needs to buy 60 liters of reagent, how much money is saved by ordering from the supplier with the lower unit price rather than the other supplier?
- 6.
A digital transcription service logs the time required to transcribe recorded audio interviews at a constant rate, recording 50 minutes of work for 20 minutes of audio, 90 minutes of work for 36 minutes of audio, and 150 minutes of work for 60 minutes of audio. A client submits a 44-minute podcast interview and a 52-minute panel discussion to be fully transcribed. If the service charges $35 per hour of transcription work, what is the total cost to transcribe both audio files?
- 7.
A passenger ferry travels between coastal islands at a constant speed. According to the ferry's navigation log, it covers 18 nautical miles in 45 minutes, 30 nautical miles in 75 minutes, and 42 nautical miles in 105 minutes. The ferry departs from Mainland Pier at 8:20 a.m. to complete a 54-nautical-mile journey to Harbor Island. If the ferry maintains this constant speed, at what time will it arrive at Harbor Island?
- 8.
An artisan bakery uses a ratio table to mix sourdough dough by combining flour and water at a constant rate. According to the bakery's log, 400 grams of flour requires 280 grams of water, 650 grams of flour requires 455 grams of water, and 900 grams of flour requires 630 grams of water. For a special catering order, a baker prepares a single batch of dough that has a combined mass of 8,500 grams of flour and water. How many grams of flour are used to make this batch of dough?
- 9.
An apiary uses a centrifugal extractor to harvest raw honey from honeycomb frames at a constant rate. According to the harvest log, 16 frames yield 24 kilograms of honey, 28 frames yield 42 kilograms of honey, and 40 frames yield 60 kilograms of honey. If the beekeeper extracts honey from 64 frames and packages the entire batch into jars that each hold 400 grams (0.4 kilograms), how many jars can be completely filled?
- 10.
A mountain rescue drone ascends vertically at a constant speed to deliver medical supplies. According to its flight test log, the drone ascends 45 meters in 18 seconds, 100 meters in 40 seconds, and 175 meters in 70 seconds. The drone launches from an observation platform at an elevation of 280 meters and climbs directly to a mountain shelter at an elevation of 730 meters. How many seconds does the drone take to make this climb?
- 11.
A cyclist calibrates an electronic odometer using a ratio table that relates the number of wheel rotations to the distance traveled. According to the calibration log, 25 rotations correspond to 55 meters, 60 rotations correspond to 132 meters, and 140 rotations correspond to 308 meters. The cyclist then rides 4 complete laps around an outdoor velodrome track where each lap measures 385 meters. How many wheel rotations does the odometer record for this entire ride?
- 12.
A trail maintenance crew uses crushed gravel to build an elevated pathway through a wetland reserve. According to the project ratio table, 28 wheelbarrow loads of gravel cover 16 meters of pathway, 63 loads cover 36 meters, and 105 loads cover 60 meters at a constant rate. The crew plans to surface an 88-meter main trail and a 24-meter scenic overlook spur. If the crew already has 145 wheelbarrow loads of gravel delivered at the trailhead, how many additional wheelbarrow loads are needed to complete both segments?
- 13.
A textile workshop uses two digital fabric printers, Model X and Model Y, that each print at a constant rate. According to the workshop log, Model X produces 84 meters of fabric in 12 minutes, 140 meters in 20 minutes, and 210 meters in 30 minutes. Model Y operates at a constant rate that is 2 meters per minute faster than Model X. If both printers run continuously at the same time for 40 minutes, what is the total length of fabric, in meters, produced by the two printers combined?
- 14.
An electric delivery van consumes battery energy at a constant rate according to the fleet log, which records 15 kilowatt-hours (kWh) consumed for 60 kilometers, 25 kWh for 100 kilometers, and 40 kWh for 160 kilometers. A driver begins the morning with a fully charged 52 kWh battery pack before completing a morning route of 76 kilometers and an afternoon route of 92 kilometers. How many kilowatt-hours of battery energy remain when the van finishes both delivery routes?
- 15.
A 3D printer uses plastic filament to manufacture small gears at a constant rate. According to the production log, the printer consumes 45 millimeters of filament to make 3 small gears, 105 millimeters to make 7 small gears, and 180 millimeters to make 12 small gears. A technician configures the printer to produce a larger gear that requires 4 times as much filament as a single small gear. How many millimeters of filament are needed to print 6 of these larger gears?
- 16.
A water desalination unit processes seawater into purified freshwater at a constant rate. According to the facility's ratio table, the unit produces 36 liters of purified water from 45 liters of seawater, 84 liters from 105 liters, and 132 liters from 165 liters. If the facility feeds 220 liters of seawater into the unit, how many liters of concentrated brine wastewater are separated and discarded?
- 17.
A commercial bakery uses an automated packaging line that packs flour into sacks at a constant rate. According to the equipment log, the line packs 192 sacks in 16 minutes, 300 sacks in 25 minutes, and 432 sacks in 36 minutes. On Tuesday, the machine operates for 35 minutes before pausing for a scheduled 15-minute maintenance break. How many additional minutes must the machine run after the break to complete a total order of 816 sacks?
- 18.
A community recycling center exchanges sorted aluminum cans for cash credits using a constant rate schedule. According to the center's records, a participant earns 45 for 60 pounds, and 25 of his earnings to the local park fund, how much money does he take home?
- 19.
A community garden organizes its drip irrigation system using a ratio table that relates the operating time of a pump to the volume of water delivered, recording 45 liters in 6 minutes, 105 liters in 14 minutes, and 150 liters in 20 minutes. The garden manager needs to fill an empty 225-liter reservoir and an empty 375-liter cistern using this pump operating at the same constant rate. How many total minutes must the pump run to completely fill both containers?