Ratios and rates (ratio tables, unit rate) Transitional Reasoning Practice
18 Math practice questions on Ratios and rates (ratio tables, unit rate). Questions that build towards applied reasoning.
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Questions
- 1.
A construction crew uses a heavy-duty pulley system to hoist structural beams to upper floors of a building. According to the equipment testing log, pulling 18 meters of cable through the hoist raises a beam by 3 meters, pulling 30 meters of cable raises it by 5 meters, and pulling 42 meters of cable raises it by 7 meters. A motorized winch that winds cable at a constant rate of 12 meters per minute is used to hoist a beam to an installation platform located at a height of 14 meters. How many minutes will the winch take to hoist the beam to the platform?
- 2.
A university prototyping laboratory operates a 3D printer that extrudes filament at a constant rate. According to the printer's calibration log, it consumes 105 grams of filament in 15 minutes, 196 grams in 28 minutes, and 315 grams in 45 minutes. A student uses the printer to produce 8 gears requiring 42 grams each and 6 brackets requiring 35 grams each. Operating continuously at this constant rate, how many total minutes will the printer take to produce all of these components?
- 3.
A reforestation project uses a seed-dispersal drone to plant native tree species across recovery zones. According to the drone's flight log, it disperses 4,200 seed pellets across 15 hectares, 6,720 seed pellets across 24 hectares, and 9,800 seed pellets across 35 hectares at a constant rate. The drone is scheduled to reseed two adjacent recovery zones: Sector A and Sector B. Sector A covers an area of 18 hectares, and Sector B requires 3,360 more seed pellets than Sector A. How many hectares does Sector B cover?
- 4.
A culinary workshop prepares bottles of herb marinade by mixing olive oil and vinegar according to a proportional recipe log. According to the log, 12 bottles require 1,800 mL of olive oil and 600 mL of vinegar, 20 bottles require 3,000 mL of olive oil and 1,000 mL of vinegar, and 28 bottles require 4,200 mL of olive oil and 1,400 mL of vinegar. The workshop currently has 4,800 mL of olive oil and 1,800 mL of vinegar in stock. What is the maximum number of complete bottles of marinade the workshop can prepare using only the ingredients in stock?
- 5.
An electronics recycling facility operates an automated wire-stripping machine that recovers copper wire at a constant rate proportional to running time. According to the machine's calibration log, it strips 120 meters of wire in 15 minutes, 192 meters in 24 minutes, and 280 meters in 35 minutes. The facility needs to process two separate batches of wire measuring 360 meters and 520 meters, but the operator must pause the machine for a mandatory 12-minute cooling and inspection period between the two batches. From the start of the first batch to the completion of the second batch, what is the total elapsed time in minutes?
- 6.
According to a municipal detention basin's monitoring log, an outlet weir discharges stormwater at a constant rate proportional to time: 180,000 liters in 8 hours, 315,000 liters in 14 hours, and 495,000 liters in 22 hours. During a storm, runoff enters the basin at a constant rate of 34,000 liters per hour while the weir continues draining water at its calibrated constant rate. If the storm continues steadily for 6 hours, by how many liters does the volume of water stored in the detention basin increase?
- 7.
An automated road-marking vehicle paints reflective traffic lines at a constant rate proportional to time. According to its calibration log, the vehicle paints 540 meters of line in 18 minutes, 810 meters in 27 minutes, and 1,260 meters in 42 minutes. A municipal crew must paint reflective edge lines along both sides of three newly resurfaced streets measuring 450 meters, 620 meters, and 730 meters in length. Operating continuously at this constant rate, how many minutes will the vehicle take to paint the lines on both sides of all three streets?
- 8.
A university library uses two high-speed scanners to digitize a collection of historical documents. According to the equipment logs, Scanner A digitizes 180 pages in 6 minutes and 270 pages in 9 minutes, while Scanner B digitizes 144 pages in 8 minutes and 216 pages in 12 minutes. If both scanners run simultaneously at these constant rates, how many total pages will they digitize together in 35 minutes?
- 9.
A solar-powered water desalination unit produces fresh drinking water from seawater at a constant rate proportional to time. According to the unit's operation log, it produces 48 liters of drinking water in 12 hours, 80 liters in 20 hours, and 112 liters in 28 hours. If a remote research outpost needs 288 liters of drinking water and runs the desalination unit for 8 hours each day, how many days of operation are required to produce the needed volume?
- 10.
A research expedition uses a portable solar generator to recharge standardized field battery packs at a constant rate. According to the generator's operating log, running the generator for 6 hours recharges 15 battery packs, running it for 14 hours recharges 35 battery packs, and running it for 22 hours recharges 55 battery packs. The team must recharge a total of 85 battery packs and has already operated the generator for 18 hours. How many additional hours must the solar generator run to finish recharging all 85 battery packs?
- 11.
A biochemical laboratory prepares a specialized cell culture broth by mixing liquid nutrient concentrate with sterile water. According to the laboratory's preparation chart, mixing 45 mL of nutrient concentrate with 315 mL of sterile water produces 360 mL of broth, while mixing 75 mL of concentrate with 525 mL of water produces 600 mL of broth. A researcher needs to prepare exactly 1,440 mL of this cell culture broth for an upcoming trial. How many milliliters of sterile water must the researcher use to prepare this batch?
- 12.
A commercial print shop operates two digital presses to produce student workbooks. Press 1 operates at a constant rate, recording in its production log that it prints 720 pages in 16 minutes, 1,080 pages in 24 minutes, and 1,620 pages in 36 minutes. Press 2 operates independently at a constant rate of 60 pages per minute. If both presses start at the same time to print separate identical orders of 2,700 pages each, how many fewer minutes does Press 2 take to complete its order than Press 1?
- 13.
An industrial textile mill operates automated spinning frames that convert raw cotton into yarn at a constant rate. According to the mill's production log, 18 kilograms of raw cotton yields 450 meters of yarn, 28 kilograms yields 700 meters, and 40 kilograms yields 1,000 meters. The mill receives a contract requiring 3,150 meters of yarn, and raw cotton is retrieved from storage in standardized containers holding 14 kilograms each. How many containers of raw cotton must be used to produce the required length of yarn?
- 14.
A hydroelectric plant generates electricity at a constant rate proportional to the volume of water released through its turbines. Operational logs show that releasing 45 megaliters of water produces 18 megawatt-hours (MWh) of electricity, and releasing 75 megaliters produces 30 MWh. The plant must produce a total of 84 MWh during a 24-hour cycle, and exactly 90 megaliters of water are released during the daytime shift. How many megaliters of water must be released during the nighttime shift to meet the total generation target?
- 15.
An electric delivery van's trip computer displays a proportional relationship between distance traveled and battery energy consumed, recording that traveling 72 kilometers consumes 16 kilowatt-hours (kWh) and traveling 135 kilometers consumes 30 kWh. The driver begins a 243-kilometer delivery route with a fully charged 60 kWh battery. At this constant rate of consumption, how many kilowatt-hours of battery energy will remain in the battery upon completing the route?
- 16.
An environmental station monitors runoff managed by a bioretention basin, where records show a consistent relationship: 144 gallons are filtered in 6 hours, 216 gallons in 9 hours, and 360 gallons in 15 hours. The engineering team installs an enhanced filter that processes water at a constant unit rate 7 gallons per hour faster than the original basin. How many total gallons of runoff will the enhanced filter process if it operates continuously for 18 hours?
- 17.
A commercial bakery operates two automated packaging lines that package snack boxes at constant rates. Line X packages 168 boxes in 7 minutes, while Line Y packages 270 boxes in 9 minutes. The bakery must complete an order of 840 boxes, and Line X is operated alone for the first 15 minutes before being shut down for maintenance. How many minutes must Line Y run alone to package the remaining boxes?
- 18.
An art workshop maintains a consistent ratio of linseed oil to pigment powder when mixing batches of custom paint. According to their recipe records, mixing 180 mL of oil requires 75 g of pigment, while mixing 300 mL of oil requires 125 g of pigment. If an artist wants to prepare a batch using 420 mL of oil but currently has only 150 g of pigment in the studio, how many additional grams of pigment must be purchased?
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